vault backup: 2025-01-13 17:02:14
This commit is contained in:
parent
c16b1ba58c
commit
fffbaa3441
6
.gitignore
vendored
6
.gitignore
vendored
@ -24,3 +24,9 @@ bin-release/
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||||
.smart-env
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||||
.DS_Store
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workspace.json
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||||
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||||
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# Ignore Smart Environment folder
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||||
.smart-env
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||||
3
.obsidian/community-plugins.json
vendored
3
.obsidian/community-plugins.json
vendored
@ -1,4 +1,5 @@
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||||
[
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||||
"copilot",
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||||
"obsidian-git"
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||||
"obsidian-git",
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"smart-connections"
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]
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||||
File diff suppressed because one or more lines are too long
26
.obsidian/plugins/copilot/data.json
vendored
26
.obsidian/plugins/copilot/data.json
vendored
@ -13,12 +13,12 @@
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||||
"googleApiKey": "",
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||||
"openRouterAiApiKey": "",
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||||
"defaultChainType": "llm_chain",
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||||
"defaultModelKey": "gemma2:latest|ollama",
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||||
"defaultModelKey": "phi4:latest|ollama",
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||||
"embeddingModelKey": "nomic-embed-text|ollama",
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||||
"temperature": 0.1,
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||||
"maxTokens": 1000,
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||||
"contextTurns": 15,
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||||
"userSystemPrompt": "",
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"userSystemPrompt": "翻译成中文",
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||||
"openAIProxyBaseUrl": "",
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||||
"openAIEmbeddingProxyBaseUrl": "",
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"stream": true,
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@ -43,21 +43,27 @@
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"provider": "openai",
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||||
"enabled": true,
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"isBuiltIn": true,
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||||
"core": true
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||||
"core": true,
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||||
"baseUrl": "",
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||||
"apiKey": ""
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||||
},
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||||
{
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||||
"name": "gpt-4o-mini",
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||||
"provider": "openai",
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||||
"enabled": true,
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||||
"isBuiltIn": true,
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||||
"core": true
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||||
"core": true,
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||||
"baseUrl": "",
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||||
"apiKey": ""
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||||
},
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||||
{
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||||
"name": "claude-3-5-sonnet-latest",
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||||
"provider": "anthropic",
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||||
"enabled": true,
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||||
"isBuiltIn": true,
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||||
"core": true
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||||
"core": true,
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||||
"baseUrl": "",
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||||
"apiKey": ""
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||||
},
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{
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"name": "llama3.2:latest",
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@ -78,6 +84,16 @@
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"isBuiltIn": false,
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"enableCors": true,
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"isEmbeddingModel": false
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},
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{
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"name": "phi4:latest",
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"provider": "ollama",
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"baseUrl": "https://possibly-engaged-filly.ngrok-free.app",
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"apiKey": "",
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"enabled": true,
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||||
"isBuiltIn": false,
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"enableCors": true,
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"isEmbeddingModel": false
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}
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],
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"activeEmbeddingModels": [
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21
.obsidian/plugins/smart-connections/data.json
vendored
Normal file
21
.obsidian/plugins/smart-connections/data.json
vendored
Normal file
@ -0,0 +1,21 @@
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{
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"new_user": false,
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"legacy_transformers": false,
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"enable_mobile": true,
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"actions": {
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"lookup": true
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},
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"smart_notices": {},
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"system_prompts_folder": "smart prompts",
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"smart_chat_folder": "smart-chats",
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"smart_chat_folder_last": "smart-chats",
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"chat_model_platform_key": "open_router",
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"open_router": {},
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"api_key": "",
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"excluded_headings": "",
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"folder_exclusions": "smart-chats",
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"show_full_path": false,
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"expanded_view": true,
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"language": "en",
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"version": "2.3.47"
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}
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17915
.obsidian/plugins/smart-connections/main.js
vendored
Normal file
17915
.obsidian/plugins/smart-connections/main.js
vendored
Normal file
File diff suppressed because one or more lines are too long
10
.obsidian/plugins/smart-connections/manifest.json
vendored
Normal file
10
.obsidian/plugins/smart-connections/manifest.json
vendored
Normal file
@ -0,0 +1,10 @@
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{
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"id": "smart-connections",
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"name": "Smart Connections",
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"author": "Brian Petro",
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"description": "Find links to similar notes using artificial intelligence from OpenAI.",
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"minAppVersion": "1.1.0",
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||||
"authorUrl": "https://wfhbrian.com",
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||||
"isDesktopOnly": false,
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||||
"version": "2.3.47"
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}
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968
.obsidian/plugins/smart-connections/styles.css
vendored
Normal file
968
.obsidian/plugins/smart-connections/styles.css
vendored
Normal file
@ -0,0 +1,968 @@
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/* deprecated positioning, use bottom bar instead */
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||||
.view-content > .sc-brand {
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position: fixed;
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bottom: 0;
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right: 0;
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||||
background-color: var(--titlebar-background);
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}
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.sc-brand {
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> svg,
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> p {
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display: inline;
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margin: 0 0.1rem 0 0.3rem;
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color: var(--text-muted);
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font-size: var(--font-smallest);
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line-height: 1;
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height: 0.88rem;
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width: auto;
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}
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> p > a {
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color: var(--text-muted);
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}
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}
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||||
.sc-list {
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.tree-item-self {
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cursor: pointer;
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small {
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color: var(--color-gray-40);
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||||
}
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}
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> .sc-collapsed ul {
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display: none;
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}
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||||
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||||
> .sc-collapsed span svg {
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transform: rotate(-90deg);
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}
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||||
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||||
> :not(.sc-collapsed) span svg {
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transform: rotate(0deg);
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||||
}
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> div {
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span svg {
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height: auto;
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margin: auto 0.5em auto 0;
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flex: none;
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}
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> span {
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display: inline-flex;
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width: 100%;
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padding-left: 0;
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}
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ul {
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margin: 0;
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padding-left: 1.3rem;
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}
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> a {
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display: block;
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}
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||||
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> ul > li {
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display: block;
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}
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}
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.sc-result {
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||||
> ul {
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list-style: none;
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padding-left: 0;
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}
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}
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||||
.sc-result.sc-result-plaintext {
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font-size: var(--font-ui-smaller);
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line-height: var(--line-height-tight);
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background-color: var(--search-result-background);
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border-radius: var(--radius-s);
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overflow: hidden;
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margin: var(--size-4-1) 0 var(--size-4-2);
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||||
color: var(--text-muted);
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||||
box-shadow: 0 0 0 1px var(--background-modifier-border);
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||||
|
||||
& > * li {
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||||
cursor: var(--cursor);
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position: relative;
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||||
padding: var(--size-4-2) var(--size-4-5) var(--size-4-2) var(--size-4-3);
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||||
white-space: pre-wrap;
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||||
width: 100%;
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||||
border-bottom: 1px solid var(--background-modifier-border);
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||||
}
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||||
}
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||||
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||||
.sc-result:not(.sc-result-plaintext) {
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||||
cursor: pointer;
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||||
padding: var(--nav-item-padding);
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||||
padding-left: 10px;
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||||
margin-bottom: 1px;
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||||
align-items: baseline;
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||||
border-radius: var(--radius-s);
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||||
font-weight: var(--nav-item-weight);
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||||
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||||
&:hover {
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color: var(--nav-item-color-active);
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||||
background-color: var(--nav-item-background-active);
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||||
font-weight: var(--nav-item-weight-active);
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||||
}
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||||
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span {
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color: var(--h5-color);
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||||
}
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||||
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small {
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color: var(--h5-color);
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font-size: 0.8rem;
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font-weight: 500;
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}
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p {
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margin-top: 0.3rem;
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margin-bottom: 0.3rem;
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||||
}
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||||
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ul > li {
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h1 {
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font-size: 1.3rem;
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||||
}
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||||
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||||
h2 {
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||||
font-size: 1.25rem;
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||||
}
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||||
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||||
h3 {
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||||
font-size: 1.2rem;
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||||
}
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||||
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||||
h4 {
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||||
font-size: 1.15rem;
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||||
}
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||||
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||||
h5 {
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||||
font-size: 1.1rem;
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||||
}
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||||
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||||
h6 {
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||||
font-size: 1.05rem;
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||||
}
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||||
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||||
h1,
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||||
h2,
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h3,
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||||
h4,
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||||
h5,
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||||
h6 {
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||||
margin-block-start: calc(var(--p-spacing)/2);
|
||||
margin-block-end: calc(var(--p-spacing)/2);
|
||||
}
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||||
}
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||||
}
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||||
} /* end .sc-list */
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||||
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||||
/* Only on right sidebar */
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||||
.mod-right-split .sc-list .sc-result {
|
||||
font-size: var(--font-text-size);
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||||
font-size: 0.88rem;
|
||||
}
|
||||
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||||
.sc-top-bar {
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||||
display: flex;
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||||
width: 100%;
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||||
justify-content: end;
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||||
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||||
.search-input-container {
|
||||
width: calc(100% - var(--size-4-8));
|
||||
margin: 4px auto;
|
||||
}
|
||||
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||||
.sc-context {
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||||
color: var(--nav-item-color);
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||||
font-size: var(--nav-item-size);
|
||||
margin: 0.5em 0.5em 1em;
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||||
width: 100%;
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||||
}
|
||||
}
|
||||
|
||||
/* Chat */
|
||||
.sc-chat-container {
|
||||
display: flex;
|
||||
flex-direction: column;
|
||||
align-items: center;
|
||||
justify-content: flex-end;
|
||||
height: 100%;
|
||||
|
||||
.sc-top-bar-container {
|
||||
align-self: flex-end;
|
||||
display: flex;
|
||||
width: 100%;
|
||||
|
||||
.sc-chat-name-input {
|
||||
flex-grow: 1;
|
||||
}
|
||||
}
|
||||
|
||||
.sc-thread {
|
||||
display: flex;
|
||||
flex-direction: column;
|
||||
align-items: flex-start;
|
||||
height: 100%;
|
||||
width: 100%;
|
||||
overflow: hidden;
|
||||
user-select: text;
|
||||
overflow-y: auto;
|
||||
|
||||
.sc-message-container {
|
||||
border: 1px solid var(--divider-color);
|
||||
border-radius: 10px;
|
||||
margin: 0.5rem 0;
|
||||
display: flex;
|
||||
flex-direction: column;
|
||||
align-items: flex-start;
|
||||
width: 100%;
|
||||
height: 100%;
|
||||
overflow-y: auto;
|
||||
background-color: var(--background-primary-alt);
|
||||
|
||||
.sc-message {
|
||||
max-width: 90ch;
|
||||
width: 90%;
|
||||
margin: 10px;
|
||||
padding: 10px;
|
||||
border-radius: 1.5rem;
|
||||
word-break: break-word;
|
||||
|
||||
&.user {
|
||||
align-self: flex-end;
|
||||
color: var(--text-normal);
|
||||
background-color: var(--background-primary);
|
||||
}
|
||||
|
||||
&.assistant,
|
||||
&.system {
|
||||
background-color: var(--background-primary-alt);
|
||||
color: var(--text-normal);
|
||||
}
|
||||
|
||||
.sc-message-content {
|
||||
margin: 0;
|
||||
padding: 1rem;
|
||||
|
||||
> * p {
|
||||
margin: 0;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
.sc-chat-form {
|
||||
display: flex;
|
||||
padding: 0 10px 1rem 0;
|
||||
width: 100%;
|
||||
max-height: 50%;
|
||||
|
||||
.sc-chat-input {
|
||||
flex-grow: 1;
|
||||
padding: 0.88rem;
|
||||
border: none;
|
||||
border-radius: 1.5rem;
|
||||
resize: none;
|
||||
height: auto;
|
||||
min-height: 4.2lh;
|
||||
max-height: 100%;
|
||||
background-color: var(--background-primary);
|
||||
color: var(--text-normal);
|
||||
margin-right: -2.7rem;
|
||||
padding-right: 3rem;
|
||||
}
|
||||
|
||||
.sc-btn-container {
|
||||
width: 2rem;
|
||||
height: 2rem;
|
||||
margin: auto;
|
||||
|
||||
> button.send-button {
|
||||
border-radius: 99999px;
|
||||
cursor: pointer;
|
||||
outline: 2px solid transparent;
|
||||
padding: 0;
|
||||
outline-offset: 2px;
|
||||
background: none !important;
|
||||
|
||||
&:focus-visible {
|
||||
outline-color: var(--text-faint);
|
||||
box-shadow: none;
|
||||
}
|
||||
|
||||
> svg {
|
||||
> circle {
|
||||
fill: var(--text-faint);
|
||||
}
|
||||
> path {
|
||||
fill: var(--background-primary);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#settings {
|
||||
display: flex;
|
||||
flex-direction: column;
|
||||
max-width: 100%;
|
||||
width: 100%;
|
||||
}
|
||||
}
|
||||
|
||||
.sc-system {
|
||||
align-self: center;
|
||||
font-style: italic;
|
||||
color: var(--text-faint);
|
||||
}
|
||||
|
||||
.sc-msg-button {
|
||||
cursor: pointer;
|
||||
float: right;
|
||||
margin-left: 5px;
|
||||
opacity: 0.8;
|
||||
|
||||
&.cycle-branch {
|
||||
float: left;
|
||||
display: flex;
|
||||
}
|
||||
|
||||
&:hover {
|
||||
opacity: 1;
|
||||
}
|
||||
}
|
||||
|
||||
#sc-abort-button {
|
||||
cursor: pointer;
|
||||
padding: 10px;
|
||||
border-radius: 5px;
|
||||
|
||||
&:hover {
|
||||
background-color: var(--background-primary);
|
||||
}
|
||||
}
|
||||
|
||||
.sc-change {
|
||||
.sc-change-footer {
|
||||
display: flex;
|
||||
justify-content: space-between;
|
||||
align-items: center;
|
||||
|
||||
& > * {
|
||||
display: inline-block;
|
||||
color: var(--text-muted);
|
||||
font-size: var(--font-smallest);
|
||||
}
|
||||
|
||||
.sc-brand {
|
||||
position: unset;
|
||||
background-color: var(--background-primary);
|
||||
}
|
||||
}
|
||||
|
||||
.sc-variation {
|
||||
--new-content-color: hsl(124, 75%, 55%, 0.13);
|
||||
--old-content-color: hsl(3, 43%, 47%, 0.13);
|
||||
display: flex;
|
||||
align-items: flex-end;
|
||||
justify-content: space-between;
|
||||
margin: 0 -300px;
|
||||
padding: 0 300px;
|
||||
|
||||
&:has(.new-content) {
|
||||
background-color: var(--new-content-color);
|
||||
|
||||
> button {
|
||||
background-color: var(--new-content-color) !important;
|
||||
}
|
||||
}
|
||||
|
||||
&:has(.old-content) {
|
||||
background-color: var(--old-content-color);
|
||||
|
||||
> button {
|
||||
background-color: var(--old-content-color) !important;
|
||||
}
|
||||
}
|
||||
|
||||
> div {
|
||||
> *:last-child {
|
||||
margin-bottom: 0;
|
||||
}
|
||||
}
|
||||
|
||||
.old-content {
|
||||
color: var(--text-muted);
|
||||
text-decoration: line-through;
|
||||
|
||||
> *:first-child {
|
||||
margin-top: 0;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
.markdown-source-view.mod-cm6 .cm-embed-block:not(.cm-table-widget):hover:has(.sc-change) {
|
||||
overflow: unset;
|
||||
box-shadow: unset;
|
||||
cursor: unset;
|
||||
}
|
||||
|
||||
.notice .sc-notice-actions {
|
||||
display: flex;
|
||||
justify-content: space-between;
|
||||
flex-direction: row-reverse;
|
||||
}
|
||||
|
||||
.sc-chat-container {
|
||||
#settings {
|
||||
display: flex;
|
||||
flex-direction: column;
|
||||
max-width: 100%;
|
||||
width: 100%;
|
||||
}
|
||||
|
||||
.sc-config-error-notice {
|
||||
display: flex;
|
||||
align-items: center;
|
||||
justify-content: space-between;
|
||||
padding: 10px;
|
||||
background-color: #ffcccc;
|
||||
border: 1px solid #ff0000;
|
||||
border-radius: 5px;
|
||||
margin: 10px 0;
|
||||
font-size: 14px;
|
||||
font-weight: bold;
|
||||
color: #ff0000;
|
||||
width: 100%;
|
||||
|
||||
span {
|
||||
flex-grow: 1;
|
||||
}
|
||||
|
||||
button {
|
||||
margin-left: 10px;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
.sc-supporters {
|
||||
max-height: 37ch;
|
||||
border: 1px solid var(--h1-color);
|
||||
border-radius: 10px;
|
||||
padding: 10px;
|
||||
margin-left: -10px;
|
||||
box-shadow: 0 1px 0 1px var(--shadow-300);
|
||||
overflow: auto;
|
||||
text-wrap: balance;
|
||||
|
||||
> p {
|
||||
margin-top: 0;
|
||||
margin-bottom: 5px;
|
||||
}
|
||||
|
||||
> ul {
|
||||
margin-top: 5px;
|
||||
}
|
||||
|
||||
> * li {
|
||||
margin-top: 0.37em;
|
||||
}
|
||||
}
|
||||
|
||||
/* settings */
|
||||
.vertical-tab-content:has(> .sc-supporters) {
|
||||
.setting-item-control {
|
||||
> select {
|
||||
max-width: 500px;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
.sc-bottom-bar {
|
||||
position: fixed;
|
||||
bottom: 0;
|
||||
right: 0;
|
||||
left: 0;
|
||||
width: 100%;
|
||||
display: flex;
|
||||
justify-content: space-between;
|
||||
align-items: center;
|
||||
background-color: var(--titlebar-background);
|
||||
padding: 0 0.5rem;
|
||||
|
||||
.sc-brand {
|
||||
flex-shrink: 0;
|
||||
}
|
||||
|
||||
.sc-context {
|
||||
flex-grow: 1;
|
||||
font-size: var(--font-smallest);
|
||||
overflow: hidden;
|
||||
text-overflow: ellipsis;
|
||||
white-space: nowrap;
|
||||
}
|
||||
}
|
||||
|
||||
.setting-component[data-setting*="/"][data-setting*="api_key"] {
|
||||
display: none;
|
||||
}
|
||||
|
||||
.setting-component[data-setting*="gpu"]:not([data-setting*="/"]) {
|
||||
display: none;
|
||||
}
|
||||
|
||||
/* SINCE COMPONENT PATTERN SETTINGS */
|
||||
.setting-component[data-setting="is_obsidian_vault"] {
|
||||
display: none;
|
||||
}
|
||||
|
||||
.setting-component[data-setting="smart_change.active"] {
|
||||
display: none;
|
||||
}
|
||||
|
||||
.group-header {
|
||||
display: flex;
|
||||
text-wrap: nowrap;
|
||||
flex-wrap: wrap;
|
||||
align-items: baseline;
|
||||
|
||||
> h2 {
|
||||
width: 100%;
|
||||
margin-bottom: 0;
|
||||
}
|
||||
|
||||
> * {
|
||||
flex-grow: 1;
|
||||
margin-bottom: 10px;
|
||||
}
|
||||
}
|
||||
|
||||
/* SMART CHAT v2 */
|
||||
.sc-context-list {
|
||||
list-style: none;
|
||||
margin: 0;
|
||||
padding: 0 1rem 1rem;
|
||||
display: none;
|
||||
flex-direction: column;
|
||||
gap: 0.5rem;
|
||||
}
|
||||
|
||||
.sc-context-header[aria-expanded="true"] + .sc-context-list {
|
||||
display: flex;
|
||||
}
|
||||
|
||||
.sc-context-header[aria-expanded="false"] + .sc-context-list {
|
||||
display: none;
|
||||
}
|
||||
|
||||
.sc-context-toggle-icon {
|
||||
margin-left: 0.5rem;
|
||||
transition: transform 0.3s ease;
|
||||
}
|
||||
|
||||
.sc-context-header[aria-expanded="true"] .sc-context-toggle-icon {
|
||||
transform: rotate(180deg);
|
||||
}
|
||||
|
||||
.sc-context-container {
|
||||
border: 1px solid var(--divider-color);
|
||||
border-radius: 10px;
|
||||
margin: 0.5rem 0;
|
||||
background-color: var(--background-primary-alt);
|
||||
overflow: auto;
|
||||
max-width: 95%;
|
||||
margin: 10px;
|
||||
flex-shrink: 0;
|
||||
}
|
||||
|
||||
.sc-context-header {
|
||||
display: flex;
|
||||
justify-content: space-between;
|
||||
align-items: center;
|
||||
padding: 0.88rem 1rem;
|
||||
background-color: var(--background-primary);
|
||||
color: var(--text-muted);
|
||||
font-weight: var(--font-medium);
|
||||
cursor: pointer;
|
||||
user-select: none;
|
||||
|
||||
&:hover {
|
||||
background-color: var(--background-primary-hover);
|
||||
}
|
||||
|
||||
&:focus {
|
||||
outline: 2px solid var(--text-muted);
|
||||
outline-offset: 2px;
|
||||
}
|
||||
}
|
||||
|
||||
.sc-context-item {
|
||||
padding: 0.5rem;
|
||||
border-radius: var(--radius-s);
|
||||
background-color: var(--background-secondary);
|
||||
color: var(--text-normal);
|
||||
display: flex;
|
||||
justify-content: space-between;
|
||||
align-items: baseline;
|
||||
font-size: var(--font-smallest);
|
||||
|
||||
&:hover {
|
||||
background-color: var(--background-secondary-hover);
|
||||
}
|
||||
}
|
||||
|
||||
.sc-context-item-path {
|
||||
font-weight: var(--font-medium);
|
||||
text-overflow: ellipsis;
|
||||
overflow: hidden;
|
||||
white-space: nowrap;
|
||||
max-width: 70%;
|
||||
}
|
||||
|
||||
.sc-context-item-score {
|
||||
font-size: var(--font-small);
|
||||
color: var(--color-gray-40);
|
||||
}
|
||||
|
||||
/* Tool Calls Component Styles */
|
||||
.sc-tool-calls-container {
|
||||
border: 1px solid var(--divider-color);
|
||||
border-radius: 10px;
|
||||
margin: 0.5rem 0;
|
||||
background-color: var(--background-primary-alt);
|
||||
overflow: auto;
|
||||
max-width: 95%;
|
||||
margin: 10px;
|
||||
flex-shrink: 0;
|
||||
}
|
||||
|
||||
.sc-tool-call {
|
||||
margin-bottom: 0.5rem;
|
||||
|
||||
&:last-child {
|
||||
margin-bottom: 0;
|
||||
}
|
||||
}
|
||||
|
||||
.sc-tool-call-header {
|
||||
display: flex;
|
||||
justify-content: space-between;
|
||||
align-items: center;
|
||||
padding: 0.88rem 1rem;
|
||||
background-color: var(--background-primary);
|
||||
color: var(--text-muted);
|
||||
font-weight: var(--font-medium);
|
||||
cursor: pointer;
|
||||
user-select: none;
|
||||
|
||||
&:hover {
|
||||
background-color: var(--background-primary-hover);
|
||||
}
|
||||
|
||||
&:focus {
|
||||
outline: 2px solid var(--text-muted);
|
||||
outline-offset: 2px;
|
||||
}
|
||||
|
||||
&[aria-expanded="true"] .sc-tool-call-toggle-icon {
|
||||
transform: rotate(180deg);
|
||||
}
|
||||
}
|
||||
|
||||
.sc-tool-call-content {
|
||||
padding: 0.5rem 1rem;
|
||||
background-color: var(--background-secondary);
|
||||
font-size: var(--font-smallest);
|
||||
|
||||
pre {
|
||||
margin: 0;
|
||||
white-space: pre-wrap;
|
||||
word-break: break-word;
|
||||
}
|
||||
|
||||
code {
|
||||
font-family: var(--font-monospace);
|
||||
}
|
||||
}
|
||||
|
||||
/* Hide content when collapsed */
|
||||
.sc-tool-call-header[aria-expanded="false"] + .sc-tool-call-content {
|
||||
display: none;
|
||||
}
|
||||
|
||||
/* Show content when expanded */
|
||||
.sc-tool-call-header[aria-expanded="true"] + .sc-tool-call-content {
|
||||
display: block;
|
||||
}
|
||||
|
||||
/* System Message Styles */
|
||||
.sc-system-message-container {
|
||||
margin: 1rem 0;
|
||||
border: 1px solid var(--background-modifier-border);
|
||||
border-radius: 6px;
|
||||
background: var(--background-secondary);
|
||||
flex-shrink: 0;
|
||||
}
|
||||
|
||||
.sc-system-message-header {
|
||||
display: flex;
|
||||
justify-content: space-between;
|
||||
align-items: center;
|
||||
padding: 0.75rem 1rem;
|
||||
cursor: pointer;
|
||||
font-weight: 500;
|
||||
border-bottom: 1px solid transparent;
|
||||
transition: background-color 0.2s ease;
|
||||
|
||||
&:hover {
|
||||
background: var(--background-modifier-hover);
|
||||
}
|
||||
|
||||
span {
|
||||
display: flex;
|
||||
align-items: center;
|
||||
gap: 0.5rem;
|
||||
}
|
||||
|
||||
.sc-system-message-toggle-icon {
|
||||
transition: transform 0.2s ease;
|
||||
}
|
||||
|
||||
&[aria-expanded="true"] {
|
||||
border-bottom-color: var(--background-modifier-border);
|
||||
}
|
||||
}
|
||||
|
||||
.sc-system-message-content {
|
||||
padding: 1rem;
|
||||
position: relative;
|
||||
background: var(--background-primary);
|
||||
border-bottom-left-radius: 6px;
|
||||
border-bottom-right-radius: 6px;
|
||||
|
||||
.sc-system-message-text {
|
||||
font-family: var(--font-monospace);
|
||||
white-space: pre-wrap;
|
||||
word-break: break-word;
|
||||
margin-right: 2rem;
|
||||
}
|
||||
|
||||
.sc-system-message-copy {
|
||||
position: absolute;
|
||||
top: 1rem;
|
||||
right: 1rem;
|
||||
padding: 0.4rem;
|
||||
background: transparent;
|
||||
border: none;
|
||||
cursor: pointer;
|
||||
opacity: 0.6;
|
||||
transition: opacity 0.2s ease;
|
||||
|
||||
&:hover {
|
||||
opacity: 1;
|
||||
}
|
||||
|
||||
&.sc-copied {
|
||||
color: var(--text-accent);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
.sc-chat-container {
|
||||
.smart-chat-overlay {
|
||||
position: absolute;
|
||||
top: 0;
|
||||
left: 0;
|
||||
right: 0;
|
||||
bottom: 0;
|
||||
background-color: var(--background-primary-alt);
|
||||
z-index: 100;
|
||||
overflow: auto;
|
||||
|
||||
.smart-chat-overlay-header {
|
||||
display: flex;
|
||||
justify-content: flex-end;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
.sc-typing-indicator {
|
||||
display: flex;
|
||||
align-items: center;
|
||||
padding: 12px 16px;
|
||||
display: none;
|
||||
|
||||
&.visible {
|
||||
display: flex;
|
||||
}
|
||||
|
||||
.sc-typing-dots {
|
||||
display: flex;
|
||||
gap: 4px;
|
||||
|
||||
.sc-typing-dot {
|
||||
width: 8px;
|
||||
height: 8px;
|
||||
background: var(--text-muted);
|
||||
border-radius: 50%;
|
||||
animation: typing-bounce 1.4s infinite ease-in-out;
|
||||
|
||||
&:nth-child(1) {
|
||||
animation-delay: 0s;
|
||||
}
|
||||
|
||||
&:nth-child(2) {
|
||||
animation-delay: 0.2s;
|
||||
}
|
||||
|
||||
&:nth-child(3) {
|
||||
animation-delay: 0.4s;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
/* keyframes must be at root level */
|
||||
@keyframes typing-bounce {
|
||||
0%,
|
||||
80%,
|
||||
100% {
|
||||
transform: scale(0.6);
|
||||
}
|
||||
40% {
|
||||
transform: scale(1);
|
||||
}
|
||||
}
|
||||
|
||||
/* Smart Directories */
|
||||
.sg-top-bar {
|
||||
display: flex;
|
||||
justify-content: flex-end;
|
||||
}
|
||||
.sg-list {
|
||||
> .sg-collapsed .sg-directory-header svg {
|
||||
transform: rotate(-90deg);
|
||||
transition: transform 0.15s ease;
|
||||
}
|
||||
|
||||
> :not(.sg-collapsed) .sg-directory-header svg {
|
||||
transform: rotate(0deg);
|
||||
transition: transform 0.15s ease;
|
||||
}
|
||||
|
||||
.sg-directory-header {
|
||||
cursor: pointer;
|
||||
user-select: none;
|
||||
|
||||
&:hover {
|
||||
background-color: var(--nav-item-background-hover);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* Add this to handle content visibility */
|
||||
.sg-directory-item.sg-collapsed .sg-directory-content {
|
||||
display: none;
|
||||
}
|
||||
|
||||
/* Lookup */
|
||||
#sc-lookup-view {
|
||||
.sc-container {
|
||||
.sc-textarea-container {
|
||||
display: flex;
|
||||
padding: 0 10px 1rem 0;
|
||||
width: 100%;
|
||||
max-height: 50%;
|
||||
|
||||
> textarea {
|
||||
flex-grow: 1;
|
||||
padding: 0.88rem;
|
||||
border: none;
|
||||
border-radius: 1.5rem;
|
||||
resize: none;
|
||||
height: auto;
|
||||
min-height: 4.2lh;
|
||||
max-height: 100%;
|
||||
background-color: var(--background-primary);
|
||||
color: var(--text-normal);
|
||||
margin-right: -2.7rem;
|
||||
padding-right: 3rem;
|
||||
}
|
||||
.sc-textarea-btn-container {
|
||||
width: 2rem;
|
||||
height: 2rem;
|
||||
margin: auto;
|
||||
|
||||
> button.send-button {
|
||||
border-radius: 99999px;
|
||||
cursor: pointer;
|
||||
outline: 2px solid transparent;
|
||||
padding: 0;
|
||||
outline-offset: 2px;
|
||||
background: none !important;
|
||||
|
||||
&:focus-visible {
|
||||
outline-color: var(--text-faint);
|
||||
box-shadow: none;
|
||||
}
|
||||
|
||||
> svg {
|
||||
> circle {
|
||||
fill: var(--text-faint);
|
||||
}
|
||||
> path {
|
||||
fill: var(--background-primary);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* Side Panes */
|
||||
div.workspace-leaf-content[data-type^="smart-"] {
|
||||
> .view-content {
|
||||
display: flex;
|
||||
flex-direction: column;
|
||||
|
||||
.sc-overlay {
|
||||
background-color: var(--background-primary-alt);
|
||||
max-width: 100%;
|
||||
max-height: 42%;
|
||||
|
||||
&:has(.setting-component) {
|
||||
overflow-y: auto;
|
||||
padding: var(--size-4-4);
|
||||
flex: none;
|
||||
|
||||
.setting-item {
|
||||
flex-direction: column;
|
||||
align-items: flex-start;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
.sc-pro {
|
||||
.sc-settings {
|
||||
padding: var(--size-4-4);
|
||||
|
||||
textarea {
|
||||
min-height: 4rem;
|
||||
flex-grow: 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
124
.obsidian/workspace.json
vendored
124
.obsidian/workspace.json
vendored
@ -4,17 +4,70 @@
|
||||
"type": "split",
|
||||
"children": [
|
||||
{
|
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"id": "36813d593e21ae7d",
|
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"id": "ec0d65b5f47f4a2a",
|
||||
"type": "tabs",
|
||||
"dimension": 54.99075785582255,
|
||||
"children": [
|
||||
{
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||||
"id": "68c5e0f8a25c828e",
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"id": "1a2e30cb0e3c6114",
|
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"type": "leaf",
|
||||
"state": {
|
||||
"type": "empty",
|
||||
"state": {},
|
||||
"type": "markdown",
|
||||
"state": {
|
||||
"file": "力学书籍/Kane-Dynamics-Theory-Applications/auto/Kane-Dynamics-Theory-Applications.md",
|
||||
"mode": "source",
|
||||
"source": false
|
||||
},
|
||||
"icon": "lucide-file",
|
||||
"title": "新标签页"
|
||||
"title": "Kane-Dynamics-Theory-Applications"
|
||||
}
|
||||
},
|
||||
{
|
||||
"id": "90e8c086546a43bc",
|
||||
"type": "leaf",
|
||||
"state": {
|
||||
"type": "markdown",
|
||||
"state": {
|
||||
"file": "多体+耦合求解器/Kane方法.md",
|
||||
"mode": "source",
|
||||
"source": false
|
||||
},
|
||||
"icon": "lucide-file",
|
||||
"title": "Kane方法"
|
||||
}
|
||||
},
|
||||
{
|
||||
"id": "0f7e37da67e92e6a",
|
||||
"type": "leaf",
|
||||
"state": {
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"title": "Kane方法 的大纲"
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88
copilot-conversations/中文回复@20250113_144007.md
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---
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||||
|
||||
**ai**: This passage discusses the challenges and solutions in teaching graduate-level dynamics, particularly focusing on the need for a robust notation system to handle complex multi-body systems.
|
||||
|
||||
Here's a breakdown of the key points:
|
||||
|
||||
* **Problem with Traditional Dynamics Education:** Graduate students often lack practical experience applying dynamics principles to real-world problems, especially those involving multiple interconnected bodies. This gap stems from a focus on theoretical concepts rather than hands-on problem-solving.
|
||||
* **Need for Effective Notation:** Analyzing complex systems requires clear and unambiguous notation to differentiate between various angular velocities, accelerations, and positions of different bodies within a system.
|
||||
* **Proposed Solution: Consistent Notational System:** The author advocates for a specific notational convention using superscripts to clearly identify the reference frame and the body in question. This system helps avoid confusion when dealing with multiple interconnected rigid bodies.
|
||||
|
||||
**Example:**
|
||||
|
||||
The passage illustrates this notation with a simple example of two rigid bodies, A and B, connected within a larger system. It demonstrates how superscripts are used to distinguish the angular velocity of each body relative to different reference frames (e.g., $\mathbf{\bar{N}_{C D}}\mathbf{B}$ for the angular velocity of B in reference frame N).
|
||||
|
||||
* **Emphasis on Practice:** The author stresses the importance of extensive problem-solving for mastering dynamics. The book includes numerous problems with varying levels of difficulty to reinforce theoretical concepts and develop practical skills.
|
||||
|
||||
|
||||
In essence, this passage highlights the need for a more practical and notationally robust approach to teaching graduate-level dynamics, bridging the gap between theory and real-world applications.
|
||||
|
||||
[Timestamp: 2025/01/13 14:40:07]
|
||||
|
||||
**user**: 中文回复
|
||||
[Timestamp: 2025/01/13 14:40:14]
|
||||
|
||||
**ai**: 这段文字讨论了在研究生层次上教授动力学所面临的挑战和解决方案，特别强调需要一个强大的符号系统来处理复杂的多个物体系统。
|
||||
|
||||
以下是关键点的总结：
|
||||
|
||||
* **传统动力学教育的问题:** 研究生通常缺乏将动力学原理应用于实际问题的实践经验，尤其是在涉及多个相互连接的物体的方面。这种差距源于对理论概念的关注而不是动手解决问题。
|
||||
* **有效符号的需求:** 分析复杂系统需要清晰、明确的符号来区分不同物体在系统中的各种角速度、加速度和位置。
|
||||
* **提出的解决方案：一致的符号系统:** 作者主张使用特定符号约定，利用上标清楚地标识参考系和相关物体。这种系统有助于避免处理多个相互连接刚体时出现的混乱。
|
||||
|
||||
**示例:**
|
||||
|
||||
这段文字用两个相互连接的刚体 A 和 B 的简单例子来说明这种符号，展示了如何使用上标来区分每个物体相对于不同参考系的角速度（例如，$\mathbf{\bar{N}_{C D}}\mathbf{B}$ 表示 B 在参考系 N 中的角速度）。
|
||||
|
||||
* **强调实践:** 作者强调了通过大量解决问题来掌握动力学的必要性。这本书包含了许多难度不同的问题，以巩固理论概念并发展实际技能。
|
||||
|
||||
|
||||
总而言之，这段文字强调需要一种更实用且符号上更加稳健的方法来教授研究生层次的动力学，弥合理论与实际应用之间的差距。
|
||||
|
||||
|
||||
|
||||
|
||||
[Timestamp: 2025/01/13 14:40:36]
|
||||
|
||||
**user**: Each of the seven chapters of this book is divided into sections. A section is identified by two numbers separated by a decimal point, the first number referring to the chapter in which the section appears, and the second identifying the section within the chapter. Thus, the identifier 2.14 refers to the fourteenth section of the second chapter. A section identifier appears at the top of each page.
|
||||
|
||||
Equations are numbered serially within sections. For example, the equations in Secs. 2.14 and 2.15 are numbered (1)-(31) and (1)-(50), respectively. References to an equation may be made both within the section in which the equation appears and in other sections. In the first case, the equation number is cited as a single number; in the second case, the section number is included as part of a threenumber designation. Thus, within Sec. 2.14, Eq. (2) of Sec. 2.14 is referred to as Eq. (2); in Sec. 2.15, the same equation is referred to as Eq. (2.14.2). To locate an equation cited in this manner, one may make use of the section identifiers appearing at the tops of pages.
|
||||
|
||||
Figures appearing in the chapters are numbered so as to identify the sections in which the figures appear. For example,the two figures in Sec. 4.8 are designated Fig. 4.8.1 and Fig. 4.8.2. To avoid confusing these figures with those in the problem sets and in Appendix I, the figure number is preceded by the letter $\mathbf{P}$ in the case of problem set figures, and by the letter A in the case of Appendix I figures. The double number following the letter P refers to the problem statement in which the figure is introduced. For example, Fig. P12.3 is introduced in Problem 12.3. Similarly, Table 3.4.1 is the designation for a table in Sec. 3.4, and Table P14.6.2 is associated with Problem 14.6.
|
||||
翻译成中文
|
||||
[Timestamp: 2025/01/13 14:41:39]
|
||||
|
||||
**ai**: 这本书的七个章节每个都分为若干小节。一个小节由两个数字用小数点隔开标识，第一个数字表示该小节所在的章节，第二个数字表示该章节中的小节序号。例如，标识 2.14 指的是第二章第十四小节。每个页面的顶部都会显示一个小节标识符。
|
||||
|
||||
在每个小节内，公式按顺序编号。例如，2.14 和 2.15 小节中的公式分别编号为 (1)-(31) 和 (1)-(50)。引用一个公式可以在它出现的章节和小节中，以及其他章节中进行。前一种情况下，公式编号仅用单个数字表示；后一种情况下，会将小节编号作为三个数字的一部分包含在内。例如，在 2.14 小节中，2.14 小节的公式 (2) 被称为公式 (2)；而在 2.15 小节中，相同的公式被称为公式 (2.14.2)。要查找以这种方式引用的公式，可以使用页面顶部的章节标识符。
|
||||
|
||||
出现在章节中的图像是按编号来标识它们所在的章节。例如，4.8 小节中的两个图像分别标记为 Fig. 4.8.1 和 Fig. 4.8.2。为了避免将这些图像与习题集和附录 I 中的图像混淆，如果是在习题集中出现的图像是用字母 $\mathbf{P}$ 前缀，如果是来自附录 I 的图像是用字母 A 前缀。双重数字跟随字母 P 指的是引入了该图像的问题陈述。例如，Fig. P12.3 是在问题 12.3 中引入的。类似地，Table 3.4.1 是 3.4 小节中的表格，而 Table P14.6.2 与问题 14.6 相关联。
|
||||
|
||||
|
||||
|
||||
|
||||
[Timestamp: 2025/01/13 14:42:10]
|
||||
|
||||
**user**: # DIFFERENTIATION OF VECTORS
|
||||
|
||||
The discipline of dynamics deals with changes of various kinds, such as changes in the position of a particle in a reference frame, changes in the configuration of a mechanical system, and so forth. To characterize the manner in which some of these changes take place, one employs the differential calculus of vectors, a subject that can be regarded as an extension of material usually taught under the heading of the differential calculus of scalar functions. The extension consists primarily of provisions made to accommodate the fact that reference frames play a central role in connection with many of the vectors of interest in dynamics. For example, let $\pmb{A}$ and $\pmb{B}$ be reference frames moving relative to each other, but having one point $o$ in common at all times, and let $\pmb{P}$ be a point fixed in $\pmb{A}$ , and thus moving in B. Then the velocity of $\pmb{P}$ in $\pmb{A}$ is equal to zero, whereas the velocity of $\pmb{P}$ in $\pmb{B}$ differs from zero. Now, each of these velocities is a time-derivative of the same vector, ${\mathfrak{r}}^{o r}.$ the position vector from $^o$ to $\pmb{P}_{\cdot}$ Hence, it is meaningless to speak simply of the time-derivative of ${\mathsf{r}}^{o P}$ . Clearly, therefore, the calculus used to differentiate vectors must permit one to distinguish between differentiation with respect to a scalar variable in a reference frame $\pmb{A}$ and differentiation with respect to the same variable in a reference frame $\pmb{B}.$
|
||||
|
||||
When working with elementary principles of dynamics, such as Newton's second law or the angular momentum principle, one needs only the ordinary differential calculus of vectors, that is, a theory involving differentiations of vectors with respect to a single scalar variable, generally the time. Consideration of advanced principles of dynamics, such as those presented in later chapters of this book, necessitates, in addition, partial differentiation of vectors with respect to several scalar variables, such as generalized coordinates and generalized speeds. Accordingly, the present chapter is devoted to the exposition of definitions, and consequences of these definitions, needed in the chapters that follow.
|
||||
翻译成中文
|
||||
[Timestamp: 2025/01/13 14:47:51]
|
||||
|
||||
**ai**: # 向量的微分
|
||||
|
||||
动力学这一学科涉及各种变化，例如粒子在参考系中位置的变化、机械系统配置的变化等。为了描述这些变化的方式，我们使用向量微积分，这可以视作对通常教授的标量函数微积分材料的扩展。这种扩展主要是为了适应参考系在动力学中许多感兴趣的向量问题中起着核心作用的事实。例如，设 $\pmb{A}$ 和 $\pmb{B}$ 是彼此相对移动但始终有一个共同点 $o$ 的参考系，并设 $\pmb{P}$ 是固定在 $\pmb{A}$ 中的一点，因而在 $\pmb{B}$ 中是运动的。那么，在 $\pmb{A}$ 中 $\pmb{P}$ 的速度为零，而在 $\pmb{B}$ 中 $\pmb{P}$ 的速度不为零。现在，这两个速度都是相同向量 ${\mathfrak{r}}^{o r}$ 关于时间的导数，即从 $^o$ 到 $\pmb{P}$ 的位置矢量。因此，不能简单地谈论 ${\mathsf{r}}^{o P}$ 关于时间的导数。显然，用来微分向量的计算必须允许我们区分在参考系 $\pmb{A}$ 中关于标量变量的微分和在相同变量中但是参考系 $\pmb{B}$ 的微分。
|
||||
|
||||
在应用动力学的基本原理时，如牛顿第二定律或角动量原理，只需要普通向量微积分，即关于单一标量变量（通常是时间）的向量微分理论。考虑到更高级的动力学原理，如本书后续章节中所呈现的，还需对向量进行多个标量变量（例如广义坐标和广义速度）的偏导数。因此，本章专门讨论了在接下来的章节中需要的定义及其推论。
|
||||
|
||||
---
|
||||
|
||||
如果您有任何关于这一主题的具体问题或需要进一步的解释，请随时告诉我！
|
||||
[Timestamp: 2025/01/13 14:49:03]
|
||||
@ -1,304 +0,0 @@
|
||||
[
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The following are transformation equations defining the angular orientation of each coordinate system inherent in FAST. ",
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Before providing these, it is useful to discuss the transformation equation relating coordinate system $\\pmb{x}$ to coordinate system $X$ where $\\pmb{x}$ (with orthogonal axes $x_{I},\\ x_{2}$ , and $x_{3}$ ) is the coordinate system resulting from three rotations $(\\theta_{\\!\\scriptscriptstyle I},\\theta_{\\!\\scriptscriptstyle2}$ , and $\\theta_{3}$ ) about the orthogonal axes $(\\,X_{I},\\,X_{2}$ , and $X_{3}$ ) of coordinate system $X$ . With all rotation angles assumed to be small, the order of rotations does not matter and Euler angles do not need to be used. Instead, what we want, is a transformation equation that is consistent with classical Bernoulli-Euler beam theory (which assumes small rotations). The correct transformation equation is: ",
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n\\begin{array}{r}{\\left[\\!\\!\\begin{array}{c}{x_{I}}\\\\ {x_{2}}\\\\ {x_{3}}\\end{array}\\!\\!\\right]\\approx\\!\\!\\underbrace{\\left[\\!\\!\\begin{array}{c c c}{I}&{\\theta_{3}}&{-\\theta_{2}}\\\\ {-\\theta_{3}}&{I}&{\\theta_{I}}\\\\ {\\theta_{2}}&{-\\theta_{I}}&{I}\\end{array}\\!\\!\\right]}_{[\\!\\!\\begin{array}{c}{A}\\\\ {B}\\end{array}\\!\\!\\right]}\\!\\!\\left[X_{I}\\right],}\\end{array}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "where $[A]$ is referred to as the Bernoulli-Euler transformation matrix in this work. The approximation symbol $(\\approx)$ is used in place of an equals symbol $(=)$ in the above expression since $[A]$ is not orthonormal, which implies that the resulting $\\pmb{x}$ from this expression is not made up of a set of mutually orthogonal axes (all transformation matrices between sets of mutually orthogonal axes must be orthonormal). So it is evident that in place of $[A]$ , what we want is the closest orthonormal matrix to $[A]$ , which is referred to as $\\left[T r a n s M a t\\right]$ in this work. From linear algebra, we know that the closest orthonormal matrix to $[A]$ in the Frobenius Norm sense is: ",
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n\\left[T r a n s M a t\\right]{=}\\left[U\\right]\\left[V\\right]^{T},\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "where the columns of $\\left[U\\right]$ contain the eigenvectors of $\\left[A\\right]\\!\\!\\left[A\\right]^{T}$ and the columns of $\\big[V\\big]$ contain the eigenvectors of $\\left[A\\right]^{T}\\left[A\\right]$ . This result follows directly from the Singular Value Decomposition (SVD) of $[A]$ : ",
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n[A]\\!=\\!\\!\\left[U\\right]\\!\\!\\left[\\Sigma\\right]\\!\\!\\left[V\\right]^{\\scriptscriptstyle T},\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "where $\\left[\\varSigma\\right]$ is a diagonal matrix containing the singular values of $[A]$ , which are $\\sqrt{e i g e n\\nu a l u e s\\;o f\\left[A\\right]\\left[A\\right]^{T}}\\;=\\sqrt{e i g e n\\nu a l u e s\\;o f\\left[A\\right]^{T}\\left[A\\right]}\\;.$ ",
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/b2c0bc757ff696893b956868f5c253bf5635452cfb9931e91b125836026cce64.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "This was derived symbolically by J. Jonkman by computing $\\left[U\\right]\\!\\!\\left[V\\right]^{T}$ by hand with verification in Mathematica. ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tower Base / Platform Coordinate System ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/88207e1709e48057eba3e20a48c5537a392d9b45b23b859db0e1ec4e12258df7.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tower Element-Fixed Coordinate System ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/3242641825dce121996aa8b64d069f719111b388bf56b4d23f53af451eb49b9d.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tower-Top / Base Plate Coordinate System ",
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/e15be66677d4a32e794cee5226c75216651a32afe750bafa3f1e124e9814b9c2.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Nacelle / Yaw Coordinate System${\\pmb d}_{t}$ cos (qYaw) 0 −sin (qYaw) b${\\pmb d}_{2}$ 0 1 0 b${\\pmb d}_{3}$ sin (qYaw) 0 cos (qYaw) b",
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "",
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Rotor-Furl Coordinate System ",
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "table",
|
||||
"img_path": "images/a25275aa7e7c67a744b5425189c4f767da676d7cf3ad526cc4f418377dae534f.jpg",
|
||||
"table_caption": [],
|
||||
"table_footnote": [],
|
||||
"table_body": "\n\n<html><body><table><tr><td>-cos +COs rf RFrlSkew)cos rf2 +sin rf3 COS RFrlSkew)sin +sin RFrlTilt)</td><td>RFrlSkew)cos RFrlTilt RFrlSkew)cos COS 9RFrl COS RFrlSkew)cos RFrlTilt -sin RFrlSkew)cos RFrlTilt RFrlTilt 1-cos sin 9RFr! OS RFrlSkew)cos RFrlTilt sin 9RFr! RFrlSkew)cos RFrlTilt cos(qRFrl )- 1] sin RFrlSkew)cos sin 9RFrl RFrlSkew)cos</td><td>RFrlTilt sin RFrlTilt L 1-cos 9RFrl COS RFrlTilt sin -sin sin RFrlTilt )cos qRFrl +sin RFrlTilt +cOS RFrlTilt sin RFrlTilt COS )-1 RFrlTilt sin qRFrl</td><td>RFrlSkew)sin RFrlSkew)cos RFrlTilt )-1] qRFrl RFrlTilt )sin( 9RFrl RFrlSkew)cos RFrlTilt RFrlTilt -1 sin qRFrl d RFrlSkew)cos RFrlTilt sin 9RFrl 1-sin RFrlSkew)cos RFrlTilt COS 9RFrl +sin RFrlSkew)cos RFrlTilt</td></tr></table></body></html>\n\n",
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Shaft Coordinate System ",
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "$c_{I}$ cos (ShftSkew) cos (ShftTilt) sin (ShftTilt) −sin (ShftSkew) cos (ShftTilt) rf $c_{2}$ cos (ShftSkew) sin (ShftTilt) cos (ShftTilt) sin (ShftSkew) sin (ShftTilt) $c_{3}$ sin (ShftSkew) 0 cos (ShftSkew) rf3 ",
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Azimuth Coordinate System $e_{I}$ 0 0 $c_{I}$ $e_{2}$ 0 cos (qDrTr+qGeAz) sin (qDrTr+qGeAz) $c_{2}$ e 0 −sin (qDrTr+qGeAz) cos (qDrTr+qGeAz) ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Teeter Coordinate System cos (qTeet 0 −sin (qTeet 0 1 0 sin (qTeet) 0 cos (qTeet) ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Hub / Delta-3 Coordinate System ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "0 \n$g_{I}$ 0 cos (Delta3) sin( Delta3) \n$g_{2}$ \n$\\pmb{g}_{3}$ 0 −sin( Delta3) cos (Delta3) ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Hub (Prime) Coordinate System ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "g'1B1 1 0 0 g1 \ng'2B1 = 0 1 0 g2 \ng B1 3 0 0 1 g3 ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equation for ${\\pmb g}^{\\,\\circ\\!B2}$ of blade 2 is similar. ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "table",
|
||||
"img_path": "images/c58123a3c912b476c777ac6b8b7934758d48845589f5d7b943273ae8335d88e8.jpg",
|
||||
"table_caption": [
|
||||
"Coned Coordinate System "
|
||||
],
|
||||
"table_footnote": [],
|
||||
"table_body": "\n\n<html><body><table><tr><td>B1 B1 2 B1 3</td><td>PreCone (1)] PreCone (1)] sin</td><td>-sin 1 COS</td><td>PreCone ()]] PreCone (1)]</td><td>g B1 1 B1 g 2 g B1 3</td></tr></table></body></html>\n\n",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equation for $i^{B2}$ is similar. ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Blade / Pitched Coordinate System ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/a2a9c533925e493d652a0d69730b87a5df026cde2fee0e7d5f9aaa614a8fa533.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equation for $j^{B2}$ is similar. ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Blade Coordinate System Aligned with Local Structural Axes (not element fixed) ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Lj1B1(r ) cos θSB1(r ) −sinθSB1(r ) iB1 \nLj2B1 (r ) θSB1(r ) cosθSB1(r ) B sin \n$\\left\\lfloor L j_{3}^{B I}\\left(r\\right)\\right\\rfloor$ B 0 0 ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equation for $L j^{B2}(r)$ is similar. ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Blade Element-Fixed Coordinate System Aligned with Local Structural Axes ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n\\begin{array}{r}{\\left[n_{I}^{B I}\\left(r\\right)\\right]}\\\\ {\\left.\\left|n_{2}^{B I}\\left(r\\right)\\right\\rangle=\\left[T r a n s M a t\\left(\\theta_{I}=\\theta_{x}^{B I}\\left(r\\right),\\theta_{2}=\\theta_{y}^{B I}\\left(r\\right),\\theta_{3}=0\\right)\\right]\\left[L j_{2}^{B I}\\left(r\\right)\\right\\rangle\\right.}\\\\ {\\left.\\left|n_{3}^{B I}\\left(r\\right)\\right\\rangle\\right]}\\end{array}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "where, ",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/cf71b1f3353b9439b47212c215710ee64d1df808df03c0029378347d198cafb7.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equation for ${\\pmb n}^{B2}(r)$ is similar. ",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Blade Element-Fixed Coordinate System Used for Calculating and Returning Aerodynamic Loads This coordinate system is coincident with $i^{B I}$ when the blade is undeflected. ",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/402bb29e7129df0062d48b3c5d723765784131fb70c72e23f07e9c78b7e694af.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equation for $m^{B2}(r)$ is similar. ",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Blade Element-Fixed Coordinate System Aligned with Local Aerodynamic Axes (i.e., chordline) / Trailing Edge Coordinate System ",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/b7bec12025e6f227efffe993d420000c18ea244ff8bae921c771471511c7eeae.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equation for $t e^{B2}(r)$ is similar. ",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tail-Furl Coordinate System ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/533bb40e8037410168158086acafc99d91b7370bfc9c854092d68c0b8bfaea2e.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tail Fin Coordinate System ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/326d9d71696178edb5d7849627247735ea5edae14d157ee4fcf3753eb8210851.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 6
|
||||
}
|
||||
]
|
||||
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Load Diff
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Load Diff
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@ -1,571 +0,0 @@
|
||||
[
|
||||
{
|
||||
"type": "text",
|
||||
"text": "There are several points on a 2-bladed turbine: Z (platform reference), Y (platform mass center), T (tower node), O (tower-top / base-plate / yaw bearing mass center), U (nacelle mass center), V (arbitrary point on rotor-furl axis), W (arbitrary point on tail-furl axis), D (center of mass of structure that furls with the rotor [not including rotor]), IMU (nacelle inertial measurement unit), P (teeter pin), SG [shaft strain gage location: i.e., a point on the shaft a distance ShftGagL towards the nacelle from point P (or point Q for a 3-blader since point P does not exist)], Q (apex of coning angle), C (hub mass center), S1 (blade node for blade 1), S2 (blade node for blade 2), I (tail boom mass center), J (tail fin mass center), and K (tail fin center-of-pressure). There are also several reference frames: E (earth / inertial), X (platform / tower base), F (tower element body), B (tower-top / base plate), N (nacelle), R (structure that furls with the rotor—generator housing, etc…), L (low speed shaft on rotor end of LSS-compliance), H (hub / rotor), M1 (blade 1 element body), M2 (blade 2 element body), G (fixed in the high speed shaft / generator), and A (tail). The following are derivations of the position vectors, angular velocities, linear velocities, partial angular velocities, partial linear velocities, angular accelerations, and linear accelerations of all these points on the 2-bladed turbine (point SG’s velocities and accelerations are not derived since they wont be used in the ensuing analysis). The velocities and accelerations of points on a 3-bladed turbine are very similar. ",
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/aea47d364c3db886f4957a49550f0ee56aef18eef7d0840dede2a171aa848949.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "ZO =[qTFA1+qTFA2]a1 + Ptfm Re f+TowerHt 21S1T1F+A(S1TT1SwSr(FTlwerxFLl) eqxT2LFA) 1qT+2SSS12T2F+AS(2TT2SSw(rTFlwerxFLl) exqT2LF) A2qT2+SS 22S+1T2F2AS(1T2TSSw(rTFwlerxFLle) xqLTF) A1qTqSTSF1Aq2TSS 2 u +[qTSS1+qTSS 2]a3 ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "OU =NacCMxnd1+NacCMznd2−NacCMynd3 rVD=(RFrlCMxn−RFrlPntxn)rf1+(RFrlCMzn−RFrlPntzn)rf2−(RFrlCMyn−RFrlPntyn)rf3 rVIMU= $\\big(N c I M U x n-R F r l P n t x n\\big)r f_{I}+\\big(N c I M U z n-R F r l P n t z n\\big)r f_{J}-\\big(N c I M U y n-R F r l P n t y n+R F r l P n t z n\\big)$ )rf3 rVP= −RFrlPntxnrf1+(Twr2Shft−RFrlPntzn)rf2−(Yaw2Shft−RFrlPntyn)rf3+OverHangc1 ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/f0aa977f81135ff9ada5ba5bbff16d69e441e535ce42fa7471ef27b93ae21afb.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "PSG = ShftGagLc ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "PQ= −UndSlingg rQC=HubCMg ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n\\begin{array}{r l}&{\\Bigr|\\int_{I}^{B I}+\\Bigr[\\psi_{I}^{B I}\\left(r\\right)q_{B I F I}+\\psi_{2}^{B I}\\left(r\\right)q_{B I F2}+\\psi_{3}^{B I}\\left(r\\right)q_{B I E I}\\Bigr]\\dot{j}_{2}^{B I}}\\\\ &{\\Bigr.}\\\\ &{\\Bigr.\\Bigr.\\Bigr.\\Bigr.\\qquad^{2}+S_{33}^{B I}\\left(r\\right)q_{B I E I}^{2}+2S_{I2}^{B I}\\left(r\\right)q_{B I F I}q_{B I F2}+2S_{23}^{B I}\\left(r\\right)q_{B I F2}q_{B I E I}+2S_{I3}^{B I}\\left(r\\right)q_{B I F I}q_{B I E I}\\Bigr]\\Biggr\\}.}\\end{array}\n$$$$\n\\begin{array}{l}{{\\displaystyle7.8I F I+\\phi_{2}^{B I}\\left(r\\right)q_{B I F2}+\\phi_{3}^{B I}\\left(r\\right)q_{B I E I}\\biggr]\\dot{J}_{I}^{B I}+\\left[\\psi_{I}^{B I}\\left(r\\right)q_{B I F I}+\\psi_{2}^{B I}\\left(r\\right)q_{B I F I2}+\\psi_{3}^{B I}\\left(r\\right)q_{B I E I}\\right]\\dot{J}_{I}^{B I}+\\cdots}}\\\\ {{\\displaystyle:R a d-\\frac{I}{2}\\Bigl[S_{I I}^{B I}\\left(r\\right)q_{B I F I}^{2}+S_{22}^{B I}\\left(r\\right)q_{B I F2}^{2}+S_{33}^{B I}\\left(r\\right)q_{B I E I}^{2}+2S_{I2}^{B I}\\left(r\\right)q_{B I F I}q_{B I F2}+2S_{23}^{B I}\\left(r\\right)q_{B I F}^{2}\\Bigr]\\dot{J}_{I}^{B I}\\,,}}\\end{array}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "",
|
||||
"text_format": "latex",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "where, ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/ef4f76a950c8f1ce0bea0dba255bdc0dc45aee29c9c4dd7e27c2905433d614c8.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [
|
||||
"The equation for $r^{\\varrho s2}\\left(r\\right)$ is similar. "
|
||||
],
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Note limit on r : 0≤r≤TipRad−HubRad=BldFlexL ",
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n\\pmb{r}^{o w}=T F r l P n t x n\\pmb{d}_{\\jmath}+T F r l P n t z n\\pmb{d}_{\\jmath}-T F r l P n t y n\\pmb{d}_{\\jmath}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "$r^{\\prime\\prime}=\\left(B o o m C M x n-T F r l P n t x n\\right)t f_{I}+\\left(B o o m C M z n-T F r l P n t z n\\right)t f_{J}-\\left(B o o m C M y n-T F r u n t z n\\right)t f_{I}=0.$ TFrlPntyn)tf3 ",
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\nr^{\\mu\\nu}=\\left(T F i n C M x n-T F r l P n t x n\\right)t f_{I}+\\left(T F i n C M z n-T F r[P n t z n)t f_{J}-\\left(T F i n C M y n-T F i n C M z n\\right)t f_{I}\\right).\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\nr^{W K}=\\left(T F i n C P x n-T F r l P n t x n\\right)t f_{I}+\\left(T F i n C P z n-T F r l P n t z n\\right)t f_{2}-\\left(T F i n C P y n-T F r u n t z n\\right)t f_{I}.\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Angular Velocities: ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "${\\}\\pmb{\\omega}^{X}=\\dot{q}_{R}\\pmb{\\Sigma}_{I}+\\dot{q}_{Y}\\pmb{\\Sigma}_{2}-\\dot{q}_{P}\\pmb{\\Sigma}_{3}$ ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "EωF( h)=EωX dφ1TSS ( h) qTSS1 + dφ2TSS ( h) qTSS 2 a dφ1 ( h) qTFA1 + dφ2TFA ( h) qTFA2 dh dh dh dh ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "dφ1TSS( h) dφ2TSS( h) dφ1TFA( h) dφ2TFA( h) ω ω qTSS1+ qTSS 2 a1 qTFA1+ qTFA2 a3 dh dh dh dh h =TwrFlexL h =TwrFlexL h =TwrFlexL h =TwrFlexL ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n{}^{E}{\\pmb\\omega}^{N}={}^{E}{\\pmb\\omega}^{B}+\\dot{q}_{\\mathrm{{}}\\scriptscriptstyle{Y a w}}{\\pmb d}_{z}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "${}^{E}{\\pmb\\omega}^{R}={}^{E}{\\pmb\\omega}^{N}+\\dot{q}_{R F r l}{\\pmb r}{\\pmb f}{\\pmb\\dot{a}}$ where, $r f\\!\\!a=\\!c o s\\left(R F r l S k e w\\right)\\!c o s\\left(R F r l T i l t\\right)\\!d_{I}+s i n\\left(R F r l T i l t\\right)\\!d_{J}-s i n\\left(R F r l T i l t\\right)\\!d_{I}-s i n\\left(R F r l T i l t\\right)\\!d_{I}+s i n\\left(R F r l T i l t\\right)\\!d_{I}.$ lSkew) cos (RFrlTilt)d3 ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n{}^{E}{\\pmb\\omega}^{L}={}^{E}{\\pmb\\omega}^{R}+\\dot{q}_{D r T r}{\\pmb c}_{I}+\\dot{q}_{G e A z}{\\pmb c}_{I}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "EωM1(r )=EωH dψ1B1(r ) dr qB1F1 +dψ2B1(r ) dr qB1F 2 dψ3B1(r ) dr qB1E1 j1B1 dφ1B1(r )qB1F1+dφ2B1(r ) qB1F 2 +dφ3B1(r ) dr qB1E1 2 ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equation for $^{E}\\pmb{\\omega}^{M2}\\left(r\\right)$ is similar. ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Since the generator is attached to the high speed shaft which may or may not rotate in the opposite direction of the low speed shaft and since $q_{G e A z}$ represents the position of the low speed shaft near the entrance of the gearbox, ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n{}^{E}{\\pmb\\omega}^{G}={}^{E}{\\pmb\\omega}^{R}+G e n D i r\\cdot G B R a t i o\\cdot{\\dot{q}}_{G e d z}{\\pmb{c}}_{I}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "where, $G e n D i r=\\binom{-I}{I}\\quad f o r\\,\\,\\,\\,G B\\,R e\\,\\nu e r s e=T r u e}\\\\ {\\,\\,\\,\\,G\\d{p}\\,\\,\\,\\,G B\\,R e\\,\\nu e r s e=F a l s e}$ ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "${}^{E}{\\pmb\\omega}^{A}={}^{E}{\\pmb\\omega}^{N}+\\dot{q}_{{}_{T F r l}}t{\\pmb f}\\dot{\\pmb u}$ where, tfa=cos (TFrlSkew) cos (TFrlTilt)d1+sin (TFrlTilt)d2−sin (TFrlSkew) cos (TFrlTilt)d3 ",
|
||||
"text_level": 1,
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Linear Velocities: ${}^{E}{\\pmb{\\nu}}^{Z}=\\dot{q}_{S g}\\bar{\\sf z}_{I}+\\dot{q}_{H\\nu}\\bar{\\sf z}_{2}-\\dot{q}_{S w}\\bar{\\sf z}_{3}$ ",
|
||||
"text_level": 1,
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n{}^{E}{\\pmb{\\nu}}^{Y}={}^{E}{\\pmb{\\nu}}^{Z}+{}^{E}{\\pmb{\\omega}}^{X}\\times{\\pmb{r}}^{Z Y}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n{}^{E}{\\nu}^{T}\\left(h\\right)={}^{E}{\\nu}^{Z}+{}^{X}{\\nu}^{T}\\left(h\\right)+{}^{E}{\\omega}^{X}\\times{r}^{Z T}\\left(h\\right)\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "where, ",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "XvT( h)=φ1TFA( h) qTFA1+φ2TFA( h) qTFA2a1 S1T1FA( h) qTFA1qTFA1+S2T2FA( h) qTFA2qTFA2+S1T2FA( h)(qTFA1qTFA2+qTFA1qTFA2) +S1T1SS( h) qTSS1qTSS1+S2T2SS( h) qTSS 2qTSS 2+S1T2SS( h)(qTSS1qTSS 2+qTSS1qTSS 2) +φ1TSS( h) qTSS1+φ2TSS( h) qTSS 2a3 ",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "${}^{E}{\\nu}^{o}={}^{E}{\\nu}^{Z}+{}^{X}{\\nu}^{o}+{}^{E}{\\omega}^{X}\\times{r}^{Z O}$ where, ",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "XvO=[qTFA1+qTFA2]a1 S1T1FA(TwrFlexL) qTFA1qTFA1+S2T2FA(TwrFlexL) qTFA2qTFA2+S1T2FA(TwrFlexL)(qTFA1qTFA2+qTFA1qTFA2) +S1T1SS(TwrFlexL) qTSS1qTSS1+S2T2SS(TwrFlexL) qTSS 2qTSS 2+S1T2SS(TwrFlexL)(qTSS1qTSS 2+qTSS1qTSS 2) +[qTSS1+qTSS 2]a3 ",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n\\begin{array}{l}{{{^E}_{\\nu}{^U}={^E}_{\\nu}{^o}+{^E}_{\\omega}{^N}\\times r^{o U}}}\\\\ {{{}}}\\\\ {{{^E}_{\\nu}{^V}={^E}_{\\nu}{^o}+{^E}_{\\omega}{^N}\\times r^{o V}}}\\\\ {{{}}}\\\\ {{{^E}_{\\nu}{^D}={^E}_{\\nu}{^V}+{^E}_{\\omega}{^R}\\times r^{V D}}}\\end{array}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equation for $E_{\\nu}^{\\phantom{\\mu\\nu}}{}^{m U}$ is similar. ",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n{}^{E}{\\pmb{\\nu}}^{P}={}^{E}{\\pmb{\\nu}}^{V}+{}^{E}{\\pmb{\\omega}}^{R}\\times{\\pmb{r}}^{V P}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "EvQ=EvP+EωH×r ",
|
||||
"text_level": 1,
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "× ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "EvS1(r )=EvQ+HvS1(r )+EωH×rQS1(r ) ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "where, ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "HvS1(r )=φ1B1(r ) qB1F1+φ2B1(r ) qB1F 2+φ3B1(r ) qB1E1j1B1+ψ1B1(r ) qB1F1+ψ2B1(r ) qB1F 2+ψ3B1(r ) qB1E1j2B1 S1B11(r ) qB1F1qB1F1+S2B21(r ) qB1F 2qB1F 2+S3B31(r ) qB1E1qB1E1 +S1B21(r )(qB1F1qB1F 2+qB1F1qB1F 2)+S2B31(r )(qB1F 2qB1E1+qB1F2qB1E1)+S1B31(r )(qB1F1qB1E1+qB1F1qB1E1) ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equation for $\\boldsymbol{\\varepsilon}_{\\boldsymbol{\\nu}}^{s_{2}}\\left(\\boldsymbol{r}\\right)$ is similar. ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n\\begin{array}{r l}&{^{E}_{\\nu}\\psi^{\\nu}=^{E}_{\\nu}\\!\\!\\!\\phantom{^{(0)}}^{\\!\\!E}\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\! \n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Partial Angular Velocities: ",
|
||||
"page_idx": 7
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Recall that: $^{E}\\!\\omega^{N_{i}}\\left(\\dot{q},q,t\\right)\\!=\\!\\!\\left(\\sum_{r=l}^{22}\\d^{E}\\omega_{r}^{N_{i}}\\left(q,t\\right)\\!\\dot{q}_{r}\\right)\\!+\\!\\;^{E}\\!\\omega_{t}^{N_{i}}\\left(q,t\\right)$ for each rigid body $N_{i}$ in the system. Note that all of the ${}^{E}{\\pmb{\\omega}}_{t}^{N_{i}}$ terms are zero as will be shown. ",
|
||||
"page_idx": 7
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "z1 for r=R z3 for r=P EωX= 7 for r=Y 0 otherwise EωtX = 0 ",
|
||||
"page_idx": 7
|
||||
},
|
||||
{
|
||||
"type": "table",
|
||||
"img_path": "images/2277d15a0b56afcd7524f8a378e1de9a8ca839f48c68db2aebeacb21a1ed8e85.jpg",
|
||||
"table_caption": [],
|
||||
"table_footnote": [],
|
||||
"table_body": "\n\n<html><body><table><tr><td rowspan=\"4\">E (h) の + E</td><td>dpi TFA h a3 for r =TFAl</td></tr><tr><td>dh dpi TSS h a1 for r =TSS1</td></tr><tr><td>dh dΦ2 TFA (h) a3 for r=TFA2</td></tr><tr><td>dh dΦ2 TSS h a for r =TSS2 dh otherwise</td></tr><tr><td colspan=\"2\">0 0F (h) =0</td></tr></table></body></html>\n\n",
|
||||
"page_idx": 7
|
||||
},
|
||||
{
|
||||
"type": "table",
|
||||
"img_path": "images/a593b4bb09ff3bcc0aa64f9fe4cad48bc1ea831df66f0ed67ed5622ce3ff0a5e.jpg",
|
||||
"table_caption": [],
|
||||
"table_footnote": [],
|
||||
"table_body": "\n\n<html><body><table><tr><td rowspan=\"4\">Q</td><td>dpIFA TFA (h) dh</td><td>a3 for r =TFAl h=TwrFlexL</td></tr><tr><td>d$iss T'SS (h) dh</td><td>for r = TSS1 h=TwrFlexL</td></tr><tr><td>dΦ2 TFA (h dh TSS</td><td>a3 for r=TFA2 h=TwrFlexL</td></tr><tr><td>dp? h dh</td><td>a for r =TSS2 h=TwrFlexL</td></tr><tr><td>E =0</td><td>0</td><td>otherwise</td></tr></table></body></html>\n\n",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "d for r=Yaw \nE ω ω 0 otherwise \nE ω ",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "rfa for r=RFrlω ω0 otherwiseE ω R =0",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/3398e4ae47d978c05d1ac6d8435467b2a54017a3ad095973c8560076ec510976.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/6312d612c59210b4b88ca58006215d23618c8c2ae4a8405023d27e07a9523168.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 9
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/fa88774625bec40d9835cefc14b9dab265ecad758ce4f53a290b13815e357f12.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 9
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equations for $^{E}\\pmb{\\omega}_{r}^{M2}\\left(r\\right)$ and $^{E}\\pmb{\\omega}_{t}^{M2}\\left(r\\right)$ are similar. ",
|
||||
"page_idx": 9
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/e31134e876cef5a881092ca70c43cba1fd09da2d674dd9f5d4cac0be697c2b35.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 9
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Partial Linear Velocities: ",
|
||||
"page_idx": 10
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Recall that: $^{E}\\nu^{X_{i}}\\left(\\dot{q},q,t\\right)=\\left(\\sum_{r=I}^{22}\\varepsilon_{r}^{\\phantom{R}}\\left(q,t\\right)\\dot{q}_{r}\\right)+^{E}\\nu_{t}^{X_{i}}\\left(q,t\\right)$ for each point $X_{i}$ in the system. Note that all of the $\\ensuremath{\\boldsymbol{\\varepsilon}}_{\\ensuremath{\\boldsymbol{\\nu}}_{t}^{X_{i}}}$ terms are zero as will be shown. ",
|
||||
"page_idx": 10
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "7 for r=Sg z3 for r=Sw for r=Hv 0 otherwise v = 0 ",
|
||||
"page_idx": 10
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "E ωr X ×r ZY for r=4,5,6 0 otherwise = 0 ",
|
||||
"page_idx": 10
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "EvrT( h)=EvrZ+ $\\begin{array}{r l r}&{\\left\\{\\begin{array}{l l}{\\varepsilon_{\\omega}^{x}\\times r^{z T}\\left(h\\right)}&{f o r}&{r=d,5,6}\\\\ {\\phi_{l}^{T R L}\\left(h\\right)a_{l}-\\left[S_{l l}^{T R L}\\left(h\\right)q_{T E A l}+S_{l2}^{T R L}\\left(h\\right)q_{T E A l}\\right]a_{2}}&{f o r}&{r=T F A l}\\end{array}\\right.}\\\\ &{\\left\\{\\begin{array}{l l}{\\phi_{l}^{T S S}\\left(h\\right)a_{3}-\\left[S_{l l}^{T S S}\\left(h\\right)q_{T S S l}+S_{l2}^{T S S}\\left(h\\right)q_{T S S2}\\right]a_{2}}&{f o r}&{r=T S S I}\\\\ {\\phi_{2}^{T R L}\\left(h\\right)a_{l}-\\left[S_{22}^{T R L}\\left(h\\right)q_{T E A2}+S_{l2}^{T R L}\\left(h\\right)q_{T E A l}\\right]a_{2}}&{f o r}&{r=T F A2}\\end{array}\\right.}\\\\ &{\\left\\}\\phi_{2}^{T R L}\\left(h\\right)a_{l}-\\left[S_{22}^{T R L}\\left(h\\right)q_{T E A2}+S_{l2}^{T R L}\\left(h\\right)q_{T E A l}\\right]a_{2}}&{f o r}&{r=T F A2}\\\\ &{\\phi_{2}^{T S S}\\left(h\\right)a_{3}-\\left[S_{22}^{T S S}\\left(h\\right)q_{T S S2}+S_{l2}^{T S S}\\left(h\\right)q_{T S S l}\\right]a_{2}}&{f o r}&{r=T S S2}\\\\ {0}&{o t h e r w i s e}\\end{array}\\right.}\\end{array}$ $\\boldsymbol{\\varepsilon}_{\\boldsymbol{\\nu}_{t}^{T}}(h)\\!=\\!\\boldsymbol{\\ O}$ ",
|
||||
"page_idx": 10
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n\\begin{array}{r}{\\left[\\begin{array}{l l l}{\\varepsilon_{\\omega}^{\\scriptscriptstyle X}\\times r^{2\\theta}}&{f o r}&{r=\\mathscr{I},\\mathscr{S},\\theta}\\\\ {a_{I}-\\Big[S_{I I}^{\\scriptscriptstyle T\\scriptscriptstyle F\\scriptscriptstyle L}\\big(T w r F l e x L\\big)q_{T r\\scriptscriptstyle A I}+S_{I2}^{\\scriptscriptstyle T\\scriptscriptstyle L}\\big(T w r F l e x L\\big)q_{T r\\scriptscriptstyle A2}\\Big]a_{2}}&{f o r}&{r=T F A I}\\\\ {a_{3}-\\Big[S_{I I}^{\\scriptscriptstyle T\\scriptscriptstyle S\\scriptscriptstyle S}\\big(T w r F l e x L\\big)q_{T r\\scriptscriptstyle S\\scriptscriptstyle I}+S_{I2}^{\\scriptscriptstyle T\\scriptscriptstyle S\\scriptscriptstyle S}\\big(T w r F l e x L\\big)q_{T r\\scriptscriptstyle S\\scriptscriptstyle S2}\\Big]a_{2}}&{f o r}&{r=T S S I}\\\\ {a_{I}-\\Big[S_{22}^{\\scriptscriptstyle T\\scriptscriptstyle E\\scriptscriptstyle A}\\big(T w r F l e x L\\big)q_{T r\\scriptscriptstyle A2}+S_{I2}^{\\scriptscriptstyle T\\scriptscriptstyle E\\scriptscriptstyle A}\\big(T w r F l e x L\\big)q_{T r\\scriptscriptstyle A I}\\Big]a_{2}}&{f o r}&{r=T F A2}\\\\ {a_{3}-\\Big[S_{22}^{\\scriptscriptstyle T\\scriptscriptstyle S\\scriptscriptstyle S}\\big(T w r F l e x L\\big)q_{T r\\scriptscriptstyle A2}+S_{I2}^{\\scriptscriptstyle T\\scriptscriptstyle S\\scriptscriptstyle S}\\big(T w r F l e x L\\big)q_{T r\\scriptscriptstyle A2}}&{f o r}&{r=T S S2}\\\\ {\\theta}&{o t h e r w i s e}\\end{array}\\right]}\\end{array}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 11
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "ω × OU for r=4,5,,11 otherwise ",
|
||||
"page_idx": 11
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "OV for r=4,5,,11 ω × otherwise EvV =0 ",
|
||||
"page_idx": 11
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/e3d6a23ac82c553a6109e1bbd076a589d53454144682502bb72c0663d0760822.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 11
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equations for $E_{\\nu_{r}}^{\\,,\\,\\,\\,\\,\\mu\\nu}$ and EvIMU are similar. ",
|
||||
"page_idx": 11
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/afa45461db2a2b95476a24dfe5f2800411c600e2ef02e1410f267618deae6c23.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 11
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/200f40a4ff42db1bfd8e7b1ddc2568d911234a08e251bb70cdd737ad06440482.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 12
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "$\\begin{array}{r l r}&{}&{f o r\\ \\ r}\\\\ &{}&{\\left\\{\\phi_{l}^{B I}\\left(r\\right)j_{l}^{B I}+\\psi_{l}^{B I}\\left(r\\right)j_{2}^{B I}-\\left[S_{1l}^{B I}\\left(r\\right)q_{B I F I}+S_{12}^{B I}\\left(r\\right)q_{B I F I}+S_{13}^{B I}\\left(r\\right)q_{B I E I}\\right]j_{3}^{B I}\\ \\ \\ f o r\\ \\ r}\\\\ &{}&{\\left\\{\\phi_{3}^{B I}\\left(r\\right)j_{l}^{B I}+\\psi_{3}^{B I}\\left(r\\right)j_{2}^{B I}-\\left[S_{33}^{B I}\\left(r\\right)q_{B I E I}+S_{23}^{B I}\\left(r\\right)q_{B I F I}+S_{13}^{B I}\\left(r\\right)q_{B I F I}\\right]j_{3}^{B I}\\ \\ \\ f o r\\ \\ r}\\\\ &{}&{\\left\\{\\phi_{2}^{B I}\\left(r\\right)j_{l}^{B I}+\\psi_{2}^{B I}\\left(r\\right)j_{2}^{B I}-\\left[S_{22}^{B I}\\left(r\\right)q_{B I F I}+S_{12}^{B I}\\left(r\\right)q_{B I F I}+S_{23}^{B I}\\left(r\\right)q_{B I E I}\\right]j_{3}^{B I}\\ \\ \\ f o r\\ \\ r}\\\\ &{}&{\\left\\{\\varepsilon_{O H}^{B I}\\times r^{Q S I}\\left(r\\right)\\right.}\\\\ &{}&{\\left.\\rho t\\rightarrow r^{r}\\left(r\\right)}\\\\ &{}&{\\left.\\rho t h e r w i\\right.}\\end{array}$ =4,5,,14 =B1F1 =B1E1 =B1F2 =Teet ise $\\boldsymbol{\\varepsilon}_{\\boldsymbol{\\nu}_{t}^{S I}}\\left(\\boldsymbol{r}\\right)=\\boldsymbol{\\ O}$ ",
|
||||
"page_idx": 12
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "",
|
||||
"text_format": "latex",
|
||||
"page_idx": 12
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equations for $^E_{\\nu_{r}^{S2}}\\left(r\\right)$ and $^E_{\\nu_{t}^{S2}}\\left(r\\right)$ are similar. ",
|
||||
"page_idx": 12
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "ω ×r OW for r=4,5,,11 0 otherwise E = 0 ",
|
||||
"page_idx": 12
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/e86624538ba5b2865e2e19027cff55cc7241673860f69c31ddc8f7297c122302.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 13
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Angular Accelerations: ",
|
||||
"page_idx": 14
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Recall that: $^{E}\\pmb{\\alpha}^{N_{i}}\\left(\\ddot{q},\\dot{q},q,t\\right)\\!=\\!\\left(\\sum_{r=l}^{22}^{E}\\pmb{\\omega}_{r}^{N_{i}}\\left(q,t\\right)\\ddot{q}_{r}\\right)\\!+\\!\\left[\\sum_{r=l}^{22}\\frac{d}{d t}\\!\\left(^{E}\\pmb{\\omega}_{r}^{N_{i}}\\left(q,t\\right)\\right)\\!\\dot{q}_{r}\\right]\\!+\\!\\frac{d}{d t}\\!\\left(^{E}\\pmb{\\omega}_{t}^{N_{i}}\\left(q,t\\right)\\right)\\!\\left(^{E}\\pmb{\\omega}_{p}^{N_{i}}\\left(q,t\\right)\\right),$ for each rigid body $N_{i}$ in the system. Note that the $\\frac{d}{d t}\\Big(^{E}\\omega_{r}^{N_{i}}\\Big)$ terms are all vector functions of $\\left({\\dot{q}},q,t\\right)$ and that all of the $\\frac{d}{d t}\\Big(^{E}\\omega_{t}^{N_{i}}\\Big)$ terms are zero as will be shown. ",
|
||||
"page_idx": 14
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n\\begin{array}{l}{\\displaystyle\\frac{d}{d t}\\Big(\\sp\\varepsilon\\omega_{r}^{X}\\Big)=O}\\\\ {\\displaystyle\\frac{d}{d t}\\Big(\\sp\\varepsilon\\omega_{{r}}^{X}\\Big)=O}\\end{array}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 14
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "$\\begin{array}{l l}{\\displaystyle\\frac{d}{d t}\\Big[^{\\varepsilon}\\pmb{\\omega}_{r}^{F}\\left(h\\right)\\Big]\\!=\\!\\left\\{\\!\\!\\begin{array}{l l}{\\displaystyle\\varepsilon_{\\pmb{\\omega}}^{\\varepsilon}\\!\\times^{\\varepsilon}\\!\\omega_{r}^{F}\\left(h\\right)}&{\\displaystyle f o r\\;\\;r=7,\\delta,...,l O}\\\\ {\\displaystyle\\theta}&{o t h e r w i s e}\\end{array}\\!\\right.}\\\\ {\\displaystyle\\frac{d}{d t}\\Big[^{\\varepsilon}\\pmb{\\omega}_{\\prime}^{F}\\left(h\\right)\\Big]=O}\\end{array}$ \n$\\begin{array}{l}{\\displaystyle\\frac{d}{d t}\\Big({}^{E}{\\omega}_{r}^{B}\\Big)=\\left\\{{\\!\\!\\begin{array}{l l}{\\displaystyle E_{{\\pm}}{\\omega}^{X}\\times{}^{E}{\\omega}_{r}^{B}}&{\\displaystyle f o r\\ \\ r=7,\\mathrm{}\\mathrm{\\it{\\mathscr{S}}},\\ldots,{\\it{\\it{10}}}}\\\\ {\\displaystyle O}&{\\ o t h e r w i s e}\\end{array}}\\right.}\\\\ {\\displaystyle\\frac{d}{d t}\\Big({}^{E}{\\omega}_{{\\iota}}^{B}\\Big)=\\cal{O}}\\end{array}$ E E N for r=Yaw \nd E ω Yaw \nω ω \ndt d otherwise \nd E \nωt =0 \ndt ",
|
||||
"page_idx": 14
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/9b38d49d69832767897ff11cc45ca36c4165b88b914426af13a479d09b6d4510.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 15
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equations for ${\\frac{d}{d t}}\\Big[^{\\,E}\\pmb{\\omega}_{r}^{{\\scriptscriptstyle M}2}\\,\\big(r\\big)\\Big]$ and d Eω $\\frac{d}{d t}\\Big[^{\\,E}\\pmb{\\omega}_{t}^{{M}2}\\left(r\\right)\\Big]$ are similar. ",
|
||||
"page_idx": 15
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/c5881e166cabde96bd49b6631c6b951f97f8b82ca05b9ad9c40af4ae957d03ed.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 16
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Linear Accelerations: ",
|
||||
"page_idx": 17
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Recall that: $\\varepsilon_{\\mathbf{}}\\boldsymbol{\\alpha}^{X_{i}}\\left(\\ddot{q},\\dot{q},q,t\\right)\\!=\\!\\!\\left(\\sum_{r=l}^{22}\\varepsilon_{\\nu_{r}^{X_{i}}}\\left(q,t\\right)\\ddot{q}_{r}\\right)\\!+\\!\\!\\left[\\sum_{r=l}^{22}\\!\\frac{d}{d t}\\!\\left({^{\\varepsilon}\\nu_{r}^{X_{i}}}\\left(q,t\\right)\\right)\\!\\dot{q}_{r}\\right]\\!+\\!\\frac{d}{d t}\\!\\left({^{\\varepsilon}\\nu_{{^I}}^{X_{i}}}\\left(q,t\\right)\\right)\\!\\left({^{\\varepsilon}\\nu_{{^I}}^{X_{i}}}\\left(q,t\\right)\\right)\\!+\\!\\frac{d}{d t}\\!\\left({^{\\varepsilon}\\nu_{{^I}}^{X_{i}}}\\left(q,t\\right)\\right)\\!+\\!{^{\\varepsilon}\\nu_{{^I}}^{X_{i}}}\\left(q,t\\right),$ for each point $X_{i}$ in the system. Note that the ${\\frac{d}{d t}}{\\Big(}^{E}\\nu_{r}^{X_{i}}{\\Big)}$ terms are all vector functions of $\\left({\\dot{q}},q,t\\right)$ and that all of the ${\\frac{d}{d t}}{\\Big(}^{E}\\nu_{t}^{X_{i}}{\\Big)}$ terms are zero as will be shown. ",
|
||||
"page_idx": 17
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n\\begin{array}{l}{\\displaystyle\\frac{d}{d t}\\Big(\\sp\\varepsilon\\pmb{\\nu}_{r}^{z}\\Big)=O}\\\\ {\\displaystyle\\frac{d}{d t}\\Big(\\sp\\varepsilon\\pmb{\\nu}_{{\\pmb\\nu}}^{z}\\Big)=O}\\end{array}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 17
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "ω ω × for r=4,5,6 v dt otherwise (EvtY) =0 dt ddt $\\iota_{\\Psi_{r}^{T}}(h)\\!\\!\\!\\int_{=\\!\\!\\!\\!\\!\\!\\int_{0}^{M}}\\!\\left[\\!\\!\\!\\begin{array}{l l l}{\\varepsilon_{\\omega_{r}^{X}\\times\\left[\\!\\!\\!\\begin{array}{l}{x}{\\nu}{\\nu^{r}\\left(h\\right)+}^{\\varepsilon}\\omega^{X}\\times r^{Z r}\\left(h\\right)\\!\\!\\right]}}&{f o r}&{r=d,5,6}\\\\ {-\\left[\\!\\!\\begin{array}{l l l}{S_{11}^{T R A}\\left(h\\right)\\dot{q}_{T r A l}+S_{12}^{T R A}\\left(h\\right)\\dot{q}_{T r A l}]\\!\\!\\right]a_{2}+}&{\\varepsilon_{\\omega}^{X}\\times^{E}\\nu_{T R A l}^{T}\\left(h\\right)}&{f o r}&{r=T R A l}\\\\ {-\\left[\\!\\!\\begin{array}{l l l}{S_{11}^{T S B}\\left(h\\right)\\dot{q}_{T S S1}+S_{12}^{T S B}\\left(h\\right)\\dot{q}_{T S S2}}\\end{array}\\right]a_{2}+}&{\\varepsilon_{\\omega}^{X}\\times^{E}\\nu_{T S S1}^{T}\\left(h\\right)}&{f o r}&{r=T S S I}\\\\ {-\\left[\\!\\!\\begin{array}{l l l}{S_{22}^{T R A}\\left(h\\right)\\dot{q}_{T R A2}+S_{12}^{T R A}\\left(h\\right)\\dot{q}_{T R A l}\\right]a_{2}+}&{\\varepsilon_{\\omega}^{X}\\times^{E}\\nu_{T R A2}^{T}\\left(h\\right)}&{f o r}&{r=T F A2}\\\\ {-\\left[\\!\\!\\begin{array}{l l l}{S_{22}^{T R A}\\left(h\\right)\\dot{q}_{T S2}+S_{12}^{T R A}\\left(h\\right)\\dot{q}_{T R A l}}\\end{array}\\right]a_{2}+}&{\\varepsilon_{\\omega}^{X}\\times^{E}\\nu_{T R S2}^{T}\\left(h\\right)}&{f o r}&{r=T F A2}\\\\ {-\\left[\\!\\!\\left[S_{22}^{T S S}\\left(h\\right)\\dot{q}_{T S S2}+S_{12}^{T S S}\\left(h\\right)\\dot{q}_{T S S1}\\right]a_{2}+}&{\\varepsilon_{\\omega}^{X}\\times^{E}\\nu_{T S S2}^{T}\\left(h\\right)}&{f o r}&{r=T S S2}\\\\ {0}&{o t h e r w i s e}\\end{array}\\right]$ d[EvtT(h )]=0 ",
|
||||
"page_idx": 17
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/7f540e8a0b94d65e0c8e85862cbfffbd9db962a124a331a6b20ff526e17acf02.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 18
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/f5e77b445b09c605b565937c9931c544ab43aea41659c32cb20fd54ba1f400a3.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 19
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equations for $\\frac{d}{d t}\\big(\\varepsilon_{\\nu_{r}^{I M U}}\\big)$ and $\\frac{d}{d t}\\big(\\boldsymbol{\\varepsilon}_{\\boldsymbol{\\nu}_{t}^{I M U}}\\big)$ are similar. ",
|
||||
"page_idx": 19
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/3ce1abcaeeff5430134d742b3e324508a553d05c8c0f30117b673678c8672d72.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 19
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/b46f6d5b32c278d5fa117b282e8e89c83efcfe951642463192021963be2383f9.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 20
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/a5ccd2c04b4bb71c7215c42e6a3f7b90011a6bd8b375fadde860693f0fd076b8.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 20
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "dtEvtS1(r )=0 ",
|
||||
"text_level": 1,
|
||||
"page_idx": 20
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The equations for $\\frac{d}{d t}\\Big[^{\\varepsilon}\\nu_{r}^{s_{2}}(r)\\Big]$ and $\\frac{d}{d t}\\Big[^{\\varepsilon}\\nu_{t}^{s2}\\left(r\\right)\\Big]$ are similar. ",
|
||||
"page_idx": 20
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/b425e4c4b9ef2bc7d01a78777fb711557ad6ceeba0f84bf46ae380326bc9c813.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 21
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/2d58bc879c460dac3de92bb198a38c050563fc9038b4acdddcdd1b0c5834c1ca.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 22
|
||||
}
|
||||
]
|
||||
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|
||||
[
|
||||
{
|
||||
"type": "text",
|
||||
"text": "The following are derivations of the output motions available in FAST for a 2-bladed turbine configuration. The motions for a 3-bladed turbine are very similar. Note that some of the motions are given multiple names in order to support variation among the user’s preferences. ",
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Blade 1 Tip Motions: \nOoPDefl1=TipDxc1=rQS1(BldFlexL)−TipRadj3B1⋅i1B1 Blade 1 OoP tip deflection (relative to rotor) (directed along the xc1-axis), (m) \nIPDefl1=TipDyc1=rQS1(BldFlexL)−TipRadj3B1⋅i2B1 Blade 1 IP tip deflection (relative to rotor) (directed along the yc1-axis), (m) \nTipDxb1=rQS1(BldFlexL)−TipRadj3B1⋅j1B1 Blade 1 flapwise tip deflection (relative to rotor) (directed along the xb1-axis), (m) \nTipDyb1=rQS1(BldFlexL)−TipRadj3B1⋅j2B1 Blade 1 edgewise tip deflection (relative to rotor) (directed along the yb1-axis), (m) \n$\\begin{array}{r}{T i p D z c I=T i p D z b I=\\Big[r^{\\varrho s I}\\left(B l d F l e x L\\right)-T i p R a d j_{3}^{B I}}\\end{array}$ $\\cdot\\dot{\\pmb{i}}_{3}^{B I}=\\left[r^{Q S I}\\left(B l d F l e x L\\right)\\!-T i p R a d\\pmb{j}_{3}^{B I}\\right.$ ⋅j3B1 Blade 1 axial tip deflection (relative to rotor) \n(directed along the zc1-/zb1-axis), (m) \n$T i p A L x b I=\\mathbf{\\nabla}^{E}a^{S I}\\left(B l d F l e x L\\right)\\cdot\\mathbf{\\boldsymbol{n}}_{I}^{B I}\\left(B l d F l e x L\\right)$ Blade 1 flapwise tip acceleration (absolute) (directed along the xb1-axis), (m/sec2) \n$T i p A L y b I=\\mathbf{\\nabla}^{E}a^{S I}\\left(B l d F l e x L\\right)\\cdot\\mathbf{\\mathbf{\\cdot}}\\mathbf{\\mathbf{}}n_{2}^{B I}\\left(B l d F l e x L\\right)$ Blade 1 edgewise tip acceleration (absolute) (directed along the yb1-axis), (m/sec2) \n$T i p A L z b I=\\mathbf{\\nabla}^{E}a^{S I}\\left(B l d F l e x L\\right)\\cdot\\mathbf{\\boldsymbol{n}}_{3}^{B I}\\left(B l d F l e x L\\right)$ Blade 1 axial tip acceleration (absolute) (directed along the zc1-/zb1-axis), (m/sec2) \n$R o l l D e j l I=T i p R D x b I=\\left(\\frac{I\\delta\\theta}{\\pi}\\right)^{H}\\!\\pmb{\\theta}^{M I}\\left(B l d F l e x L\\right)\\cdot\\pmb{j}_{I}^{B I}$ Blade 1 roll tip deflection (relative to the undeflected position), (about the xb1-axis), (deg) \n$P t c h D e j l-T i p R D y b I=\\left(\\frac{I\\,\\delta\\theta}{\\pi}\\right)^{H}\\!\\theta^{M I}\\left(B l d F l e x L\\right)\\cdot\\dot{J}_{2}^{B I}$ Blade 1 pitch tip deflection (relative to the undeflected position), (about the yb1-axis), \n(deg) ",
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "where: $^{H}\\!\\theta^{M I}\\left(B l d F l e x L\\right)=^{E}\\!\\omega_{B I F I}^{M I}\\left(B l d F l e x L\\right)q_{B I F I}+^{E}\\!\\omega_{B I E I}^{M I}\\left(B l d F l e x L\\right)q_{B I E I}+^{E}\\!\\omega_{I}^{I}\\,,$ BΜ11F2(BldFlexL) qB1F 2 where: $r^{~o s t}\\left(B l d F l e x L\\right)\\!=\\!r^{~o V}+r^{~V P}+r^{P Q}+r^{Q S I}\\left(B l d F l e x L\\right)$ ",
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/ff3b6c808f53eed30fb804e400aefda635080690456a987aad15c16d5a0b6883.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "",
|
||||
"page_idx": 0
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n{\\begin{array}{l}{S p n i A L x b{I}{\\,=\\,}^{E}a^{S t}\\left(R^{S p a n i}\\right)\\cdot{n}_{I}^{B I}\\left(R^{S p a n i}\\right)}\\\\ {1,2,...{\\,,5)},\\,(\\mathrm{m/sec}^{2})}\\\\ {S p n i A L y b{I}{\\,=\\,}^{E}a^{S t}\\left(R^{S p a n i}\\right)\\cdot{n}_{2}^{B I}\\left(R^{S p a n i}\\right)}\\\\ {1,2,...{\\,,5)},\\,(\\mathrm{m/sec}^{2})}\\\\ {S p n i A L z b{I}{\\,=\\,}^{E}a^{S t}\\left(R^{S p a n i}\\right)\\cdot{n}_{3}^{B I}\\left(R^{S p a n i}\\right)}\\\\ {1,2,...{\\,,5)},\\,(\\mathrm{m/sec}^{2})}\\end{array}}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Blade 1 local flapwise acceleration (absolute) of span station $i$ (directed along the local xb1-axis) ${\\bf\\nabla}^{i}={\\bf\\nabla}$ Blade 1 local edgewise acceleration (absolute) of span station $i$ (directed along the local yb1-axis) ${\\boldsymbol{\\mathbf{\\mathit{i}}}}=$ ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Blade 1 axial acceleration (absolute) of span station $i$ (directed along the zc1-/zb1-/local zb1-axis) $(i=$ ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Blade 2 Tip Motions: The output motions of blade 2 are similar to those of blade 1. ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/2057057aaac1479c30036b6175385a20823e1b62a204561d7dd450dc0ac8fb7a.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Blade 1 pitch angle (position) (positive towards feather / about the minus zc1- ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "/minus zb2-axis), (deg) ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Blade 2 pitch angle (position) (positive towards feather / about the minus zc2- ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Teeter Motions: ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\nT e e t D e f l=R o t T e e t P=T e e t P y a=\\left(\\frac{I\\,\\delta\\theta}{\\pi}\\right)q_{T e e t}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Rotor teeter angle (position) (about the ya-axis), (deg) ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Rotor teeter angular velocity (about the ya-axis), (deg/sec) ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Rotor teeter angular acceleration (about the ya-axis), (deg/sec) ",
|
||||
"page_idx": 1
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/5ae9ae923e89b7ee52899a62a43cb9af6327bdd5839b12f492c4132f898ce7f4.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 2
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/e1db52774350e87a4ba12810c360d943d26c454ca95528c4ecf6eee0cda1fa87.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Rotor-Furl Motions: ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "180 RotFurl=RotFurlP RF ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Nacelle IMU translational velocity (directed along the xs-axis), (m/sec) Nacelle IMU translational velocity (directed along the ys-axis), (m/sec) Nacelle IMU translational velocity (directed along the zs-axis), (m/sec) Nacelle IMU translational acceleration (directed along the xs-axis), $(\\mathrm{m/sec}^{2})$ Nacelle IMU translational acceleration (directed along the ys-axis), $(\\mathrm{m/sec}^{2})$ Nacelle IMU translational acceleration (directed along the zs-axis), $(\\mathrm{m/sec}^{2})$ ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Nacelle IMU angular (rotational) velocity (about the xs-axis), (deg/sec) ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Nacelle IMU angular (rotational) velocity (about the zs-axis), (deg/sec) Nacelle IMU angular (rotational) acceleration (about the xs-axis), (deg/sec2) Nacelle IMU angular (rotational) acceleration (about the ys-axis), (deg/sec2) Nacelle IMU angular (rotational) acceleration (about the zs-axis), (deg/sec2) ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Rotor-furl angle (position) (about the rotor-furl axis), (deg) ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Rotor-furl angular velocity (about the rotor-furl axis), (deg/sec) ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Rotor-furl angular acceleration (about the rotor-furl axis), (deg/sec2) ",
|
||||
"page_idx": 3
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/c80ac1f42a7cf2cd3aa056fddb53af0ebc8b8cdb5e5d6fbd15630e314107e179.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Nacelle yaw angle (position) (about the zn-/zp-axis), (deg) Nacelle yaw angular velocity (about the zn-/zp-axis), (deg/sec) Nacelle yaw angular acceleration (about the zn-/zp-axis), (deg/sec2) ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tower-Top Motions: ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Nacelle yaw error (about the zt-axis), (deg) ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\n\\ Y a w B r T D x p=\\Big[\\pmb{r}^{z o}-\\big(T o w e r H t+P t f m\\,R e\\,f\\big)\\pmb{a}_{2}\\Big]\\cdot\\pmb{b}_{I}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tower-top / yaw bearing translational deflection (relative to undeflected position) ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "(directed along the xp-axis), (m) \n$\\ Y a w B r T D y p=-\\Big[{r}^{Z O}-\\big(T o w e r H t+P t f m\\,R e\\,f\\big)\\,{a}_{2}\\Big]\\cdot{b}_{3}$ \n(directed along the yp-axis), (m) \n$\\ Y a w B r T D z p=\\Big[\\pmb{r}^{z o}-\\big(T o w e r H t+P t f m\\,R e\\,f\\big)\\pmb{a}_{2}\\Big]\\cdot\\pmb{b}_{2}$ \n(directed along the zp-axis), (m) \n$\\begin{array}{r}{T T D s p F A=Y a w B r T D x t=\\Big[\\underline{{r}}^{Z O}-\\big(T o w e r H t+P t f m\\,R e\\,f\\big)a_{2}\\Big]\\cdot a_{I}}\\end{array}$ \nposition) (directed along the xt-axis), (m) \n$T T D s p S S=Y a w B r T D y t=-\\Big[r^{Z O}-\\big(T o w e r H t+P t f m\\,R e\\,f\\big)a_{2}\\Big]\\cdot a_{3}$ \nundeflected position) (directed along the yt-axis), (m) \n$T T D s p A x=Y a w B r T D z t=\\left[r^{z o}-\\left(T o w e r H t+P t f m\\,R e\\,f\\right)a_{2}\\right]$ ⋅a2 \nposition) (directed along the zt-axis), (m) ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tower-top / yaw bearing translational deflection (relative to undeflected position) Tower-top / yaw bearing translational deflection (relative to undeflected position) Tower-top / yaw bearing fore-aft (translational) deflection (relative to undeflected Tower-top / yaw bearing side-to-side (translational) deflection (relative to Tower-top / yaw bearing axial (translational) deflection (relative to undeflected ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "$Y a w B r T A x p={}^{E}a^{o}\\cdot b_{_{I}}$ $Y a w B r T A y p=-\\,^{E}a^{o}\\cdot b_{s}$ $Y a w B r T A z p={}^{E}a^{o}\\cdot b_{2}$ ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tower-top / yaw bearing translational acceleration (directed along the xp-axis), (m/sec) Tower-top / yaw bearing translational acceleration (directed along the yp-axis), (m/sec) Tower-top / yaw bearing translational acceleration (directed along the zp-axis), (m/sec2) ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\nT T D s p R o l l=Y a w B r R D x t=\\left(\\frac{l\\,\\delta\\boldsymbol{\\theta}}{\\pi}\\right)^{\\,x}\\!\\!\\!\\boldsymbol{\\theta}^{B}\\cdot\\!\\boldsymbol{a}_{l}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tower-top / yaw bearing roll deflection (relative to the undeflected position) (about the xt-axis), ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "(deg) ",
|
||||
"page_idx": 4
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/b38c4988ac1e5719ff698fcbf8f729662bca9a2a8b26838cf362115222c35539.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "images/0c218afa5aa05229840608cb8327fe4452c4006430a61cd378e0c48bb48f3d00.jpg",
|
||||
"img_caption": [],
|
||||
"img_footnote": [
|
||||
"Tower Local Gage Motions: "
|
||||
],
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tower local fore-aft translational acceleration (absolute) of node $i$ (directed along the local xt-axis) $(i=$ ",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tower local side-to-side translational acceleration (absolute) of node $i$ (directed along the local yt-axis) ",
|
||||
"page_idx": 5
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tail-Furl Motions: ",
|
||||
"text_level": 1,
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "TailFurl=TailFurlP ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "image",
|
||||
"img_path": "",
|
||||
"img_caption": [],
|
||||
"img_footnote": [],
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tail-furl angle (position) (about the tail-furl axis), (deg) ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "$T a i l F u r l V=\\left(\\frac{I\\,\\!\\delta O}{\\pi}\\right)\\dot{q}_{\\scriptscriptstyle T F r l}$ $T a i l F u r l A=\\left(\\frac{I\\,\\delta0}{\\pi}\\right)\\ddot{q}_{\\scriptscriptstyle T F r l}$ ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tail-furl angular velocity (about the tail-furl axis), (deg/sec) ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tail-furl angular acceleration (about the tail-furl axis), (deg/sec2) ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Platform Motions: \n$P t f m T D x t=r^{Z}\\cdot{\\pmb a}_{I}$ \n$P t f m T D y t=-r^{Z}\\cdot{\\bf{\\boldsymbol{a}}}_{3}$ \n$P t f m T D z t=r^{Z}\\cdot{\\bf{a}}_{2}$ \nPtfmSurge=PtfmTDxi=qS g \n$P t f m S w a y=P t f m T D y i=q_{S w}$ \n$P t f m H e a\\nu e=P t f m T D z i=q_{H\\nu}$ \n$P t f m T V x t={}^{E}\\nu^{Z}\\cdot{\\bf{a}}_{I}$ \n$P t f m T V y t=-\\,^{E}\\nu^{Z}\\cdot{\\bf{a}}_{3}$ \n$P t f m T V z t={}^{E}\\nu^{Z}\\cdot{\\bf{a}}_{2}$ \nPtfmTVxi= qSg \n$P t\\/m T\\o V\\!y i=\\dot{q}_{S w}$ \nPtfmTVzi= qHv \n$P t f m T A x t={}^{E}{\\pmb{a}}^{Z}\\cdot{\\pmb{a}}_{I}$ \nPtfmTAyt= −EaZ \nPtfmTAzt= a a \nPtfmTAxi= qSg \nPtfmTAyi= qSw \nPtfmTAzi= qHv ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Platform horizontal surge displacement (directed along the xt-axis), (m) Platform horizontal sway displacement (directed along the yt-axis), (m) Platform vertical heave displacement (directed along the zt-axis), (m) Platform horizontal surge displacement (directed along the xi-axis), (m) Platform horizontal sway displacement (directed along the yi-axis), (m) Platform vertical heave displacement (directed along the zi-axis), (m) Platform horizontal surge velocity (directed along the xt-axis), (m/sec) Platform horizontal sway velocity (directed along the yt-axis), (m/sec) Platform vertical heave velocity (directed along the zt-axis), (m/sec) Platform horizontal surge velocity (directed along the xi-axis), (m/sec) Platform horizontal sway velocity (directed along the yi-axis), (m/sec) Platform vertical heave velocity (directed along the zi-axis), (m/sec) Platform horizontal surge acceleration (directed along the xt-axis), $(\\mathrm{m/sec}^{2})$ Platform horizontal sway acceleration (directed along the yt-axis), $(\\mathrm{m/sec}^{2})$ Platform vertical heave acceleration (directed along the zt-axis), $(\\mathrm{m/sec}^{2})$ Platform horizontal surge acceleration (directed along the xi-axis), $(\\mathrm{m/sec}^{2})$ Platform horizontal sway acceleration (directed along the yi-axis), $(\\mathrm{m/sec}^{2})$ Platform vertical heave acceleration (directed along the zi-axis), $(\\mathrm{m/sec}^{2})$ ",
|
||||
"page_idx": 6
|
||||
},
|
||||
{
|
||||
"type": "table",
|
||||
"img_path": "images/b59ad39bbceeabad86b89deae4877fa31e3dd12c070fc6930f2087c9303b729e.jpg",
|
||||
"table_caption": [],
|
||||
"table_footnote": [],
|
||||
"table_body": "\n\n<html><body><table><tr><td>180 PtfmRoll=PtfmRDxi= 4R π 180 PtfmPitch = PtfmRDyi qp π</td><td>Platform roll tilt displacement (about the xi-axis), (deg) Platform pitch tilt displacement (about the yi-axis), (deg)</td></tr><tr><td>180 PtfmYaw = PtfmRDzi = π</td><td>Platform yaw displacement (about the zi-axis), (deg) qy</td></tr><tr><td>180 E a</td><td></td></tr><tr><td>PtfmRVxt = π 180</td><td>Platform roll tilt velocity (about the xt-axis), (deg/sec)</td></tr><tr><td>PtfmRVyt = π 180 E</td><td>Platform pitch tilt velocity (about the yt-axis), (deg/sec)</td></tr><tr><td>PtfmRVzt = π 180</td><td>Platform yaw velocity (about the zt-axis), (deg/sec)</td></tr><tr><td>PtfmRVxi = π</td><td>Platform roll tilt velocity (about the xi-axis), (deg/sec)</td></tr><tr><td>180 PtfmRVyi = qp π</td><td>Platform pitch tilt velocity (about the yi-axis), (deg/sec)</td></tr><tr><td>180 PtfmRVzi = qy π</td><td>Platform yaw velocity (about the zi-axis), (deg/sec)</td></tr><tr><td>180 PtfmRAxt = π</td><td>Platform roll tilt acceleration (about the xt-axis), (deg/sec2)</td></tr><tr><td>180 PtfmRAyt = π</td><td>Platform pitch tilt acceleration (about the yt-axis), (deg/sec?)</td></tr><tr><td>180 PtfmRAzt = π</td><td>Platform yaw acceleration (about the zt-axis), (deg/sec²)</td></tr><tr><td>180 PtfmRAxi = YR π</td><td>Platform roll tilt acceleration (about the xi-axis), (deg/sec²)</td></tr><tr><td>180 PtfmRAyi = dip π</td><td>Platform pitch tilt acceleration (about the yi-axis), (deg/sec2)</td></tr></table></body></html>\n\n",
|
||||
"page_idx": 7
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$P t j m R A z i=\\left(\\frac{l\\,{\\delta}O}{\\pi}\\right)\\ddot{q}_{_Y}$ ",
|
||||
"text_format": "latex",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Platform yaw acceleration (about the zi-axis), (deg/sec) ",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tail-Furl Motions: ",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "$T F i n A l p h a=\\Bigg(\\frac{I\\,\\!\\!\\delta\\boldsymbol{\\theta}}{\\pi}\\Bigg)T F i n A O A$ $T F i n C L i f t=T F i n C L$ $T F i n C D r a g=T F i n C D$ $T F i n D n\\,P r\\,s=T F i n Q$ $T F i n C P F x=T F i n K F x\\,/\\,l,000$ $T F i n C P F y=T F i n K F y\\ /\\ l,O O O$ ",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Tail fin lift coefficient, (-) Tail fin drag coefficient, (-) Tail fin dynamic pressure, (Pa) Tail fin tangential force, (kN) Tail fin normal force, (kN) ",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Wind Motions: ",
|
||||
"text_level": 1,
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Wind $V x i=u$ Wind $W i n d V y i=\\nu W i n d$ Wind $V z i=w$ Wind ",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Nominal hub-height wind velocity (directed along the xi-axis), $(\\mathrm{m/s})$ Cross-wind hub-height velocity (directed along the yi-axis), $(\\mathrm{m/s})$ Vertical hub-height wind velocity (directed along the zi-axis), $(\\mathrm{m/s})$ ",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\nT o t W i n d V=\\sqrt{W i n d V x i^{2}+W i n d V y i^{2}+W i n d V z i^{2}}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Total hub-height wind velocity magnitude, $(\\mathrm{m/s})$ ) ",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "equation",
|
||||
"text": "$$\nH o r W i n d V=\\sqrt{W i n d V\\!x i^{2}+W i n d V\\!y i^{2}}\n$$",
|
||||
"text_format": "latex",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "Horizontal hub-height wind velocity magnitude (in the xi-/yi-plane), (m/s) ",
|
||||
"page_idx": 8
|
||||
},
|
||||
{
|
||||
"type": "text",
|
||||
"text": "HorWndDir Horizontal hub-height wind direction (about the zi-axis), (deg) VerWndDir Vertical hub-height wind direction (about an axis orthogonal to the zi-axis and the horizontal wind vector), (deg) ",
|
||||
"page_idx": 8
|
||||
}
|
||||
]
|
||||
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@ -81,7 +81,7 @@ ISBN0-07-037846-0
|
||||
|
||||
Preface ix To the Reader xV
|
||||
|
||||
Chapter 1 Differentiation of Vectors
|
||||
# Chapter 1 Differentiation of Vectors
|
||||
|
||||
1.1 Vector Functions 2
|
||||
1.2 Several Reference Frames 2
|
||||
@ -232,6 +232,7 @@ When either the magnitude of a vector $\mathbf{v}$ and/or the direction of v in
|
||||
|
||||
Example In Fig. 1.1.1, $\pmb{P}$ represents a point moving on the surface of a rigid sphere S, which, like any rigid body, may be regarded as a reference frame. (Reference frames should not be confused with coordinate systems. Many coordinate systems can be embedded in a given reference frame.) If $\pmb{\Psi}$ is the position vector from the center $c$ of $s$ to point $\pmb{P}$ , and if $\pmb q_{1}$ and $\pmb q_{2}$ are the angles shown, then $\pmb{\mathbf{p}}$ is a vector function of $\pmb q_{1}$ and $\pmb q_{2}$ in $\pmb{s}$ because the direction of $\pmb{\mathbb{p}}$ in $\boldsymbol{s}$ depends on $\pmb q_{1}$ and $q_{2}$ , but $\pmb{\mathsf{p}}$ is independent of $\pmb q_{3}$ in S, where $\pmb q_{3}$ is the distance from $c$ to a point $\pmb R$ situated as shown in Fig. 1.1.1. The position vector r from $c$ to $\pmb R$ is a vector function of $\pmb q_{3}$ in $\pmb{S},$ but is independent of $\pmb q_{1}$ and $\pmb q_{2}$ in S, and the position vector $\pmb q$ from $\pmb{P}$ to $\pmb R$ is a vector function of $\pmb q_{1}$ $\boldsymbol{q}_{2}$ , and $\pmb q_{3}$ in $\pmb{S}$
|
||||
|
||||
|
||||
|
||||
Figure 1.1.1
|
||||
|
||||
@ -241,10 +242,11 @@ A vector v may be a function of a variable $\pmb q$ in one reference frame, but
|
||||
|
||||
Example The outer gimbal ring $\pmb{A}$ , inner gimbal ring $\pmb{{\cal B}},$ and rotor $c$ of the gyroscope depicted in Fig. 1.2.1 each can be regarded as a reference frame. If p is the position vector from point $^o$ to a point $\pmb{P}$ of $c$ then p is a function of
|
||||
|
||||
|
||||
|
||||
Figure 1.2.1
|
||||
|
||||
$\pmb q_{1}$ both in $\pmb{A}$ and in $\pmb{B}$ but is independent of $\pmb q_{1}$ in $C;\mathfrak{p}$ is a function of $\pmb{q_{2}}$ in $\pmb{A}$ , but is independent of $\pmb{q}_{2}$ both in $\pmb{B}$ and in $c$ ; and $\pmb{\Psi}$ is independent of $\pmb q_{3}$ in each of $A,B,$ and $^c$ , but is a function of $\pmb q_{3}$ in reference frame $\pmb{D}$
|
||||
$\pmb q_{1}$ both in $\pmb{A}$ and in $\pmb{B}$ but is independent of $\pmb q_{1}$ in $C;{p}$ is a function of $\pmb{q_{2}}$ in $\pmb{A}$ , but is independent of $\pmb{q}_{2}$ both in $\pmb{B}$ and in $c$ ; and $\pmb{P}$ is independent of $\pmb q_{3}$ in each of $A,B,$ and $C$ , but is a function of $\pmb q_{3}$ in reference frame $\pmb{D}$
|
||||
|
||||
# 1.3 SCALAR FUNCTIONS
|
||||
|
||||
|
||||
@ -0,0 +1,9 @@
|
||||
# 向量的微分
|
||||
|
||||
动力学这一学科涉及各种变化，例如粒子在参考系中位置的变化、机械系统配置的变化等。为了描述这些变化的方式，我们使用向量微积分，这可以视作对通常教授的标量函数微积分材料的扩展。这种扩展主要是为了适应参考系在动力学中许多感兴趣的向量问题中起着核心作用的事实。例如，设 $\pmb{A}$ 和 $\pmb{B}$ 是彼此相对移动但始终有一个共同点 $o$ 的参考系，并设 $\pmb{P}$ 是固定在 $\pmb{A}$ 中的一点，因而在 $\pmb{B}$ 中是运动的。那么，在 $\pmb{A}$ 中 $\pmb{P}$ 的速度为零，而在 $\pmb{B}$ 中 $\pmb{P}$ 的速度不为零。现在，这两个速度都是相同向量 ${\mathfrak{r}}^{o r}$ 关于时间的导数，即从 $^o$ 到 $\pmb{P}$ 的位置矢量。因此，不能简单地谈论 ${\mathsf{r}}^{o P}$ 关于时间的导数。显然，用来微分向量的计算必须允许我们区分在参考系 $\pmb{A}$ 中关于标量变量的微分和在相同变量中但是参考系 $\pmb{B}$ 的微分。
|
||||
|
||||
在应用动力学的基本原理时，如牛顿第二定律或角动量原理，只需要普通向量微积分，即关于单一标量变量（通常是时间）的向量微分理论。考虑到更高级的动力学原理，如本书后续章节中所呈现的，还需对向量进行多个标量变量（例如广义坐标和广义速度）的偏导数。因此，本章专门讨论了在接下来的章节中需要的定义及其推论。
|
||||
|
||||
当一个向量 \(\mathbf{v}\) 的大小和/或在参考系 \(A\) 中的方向依赖于标量变量 \(q\) 时，\(\mathbf{v}\) 被称为在 \(A\) 中关于 \(q\) 的向量函数。否则，\(\mathbf{v}\) 在 \(\pmb A\) 中被认为是独立于 \(\pmb q\) 的。
|
||||
|
||||
例如，在图 1.1.1 中，\(\pmb{P}\) 表示一个点在刚体球面 \(S\) 上移动。像任何刚体一样，它可以被视为一个参考系（注意：参考系不应与坐标系统混淆；许多坐标系统可以嵌入到给定的参考系中）。如果 \(\pmb{\Psi}\) 是从球心 \(c\) 到点 \(\pmb{P}\) 的位置向量，而 \(\pmb q_{1}\) 和 \(\pmb q_{2}\) 是图中所示的角度，则在 \(S\) 中，\(\pmb{\mathbf{p}}\) 是关于 \(\pmb q_{1}\) 和 \(\pmb q_{2}\) 的向量函数，因为 \(\pmb{\mathbb{p}}\) 在 \(s\) 中的方向依赖于 \(\pmb q_{1}\) 和 \(q_{2}\)，但 \(\pmb{\mathsf{p}}\) 在 \(S\) 中独立于 \(\pmb q_{3}\)，其中 \(\pmb q_{3}\) 是从 \(c\) 到图中所示位置的点 \(\pmb R\) 的距离。从 \(c\) 到 \(\pmb R\) 的位置向量 \(\mathbf{r}\) 在 \(S\) 中是关于 \(\pmb q_{3}\) 的向量函数，但在 \(S\) 中独立于 \(\pmb q_{1}\) 和 \(\pmb q_{2}\)，而从 \(\pmb{P}\) 到 \(\pmb R\) 的位置向量 \(\pmb q\) 在 \(S\) 中是关于 \(\pmb q_{1}\), \(\boldsymbol{q}_{2}\), 和 \(\pmb q_{3}\) 的向量函数。
|
||||
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1
多体+耦合求解器/Kane方法.md
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1
多体+耦合求解器/Kane方法.md
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@ -0,0 +1 @@
|
||||
把主动力和惯性力向偏速度方向投影得到动力学方程
|
||||
66
多体+耦合求解器/动态数组调研.md
Normal file
66
多体+耦合求解器/动态数组调研.md
Normal file
@ -0,0 +1,66 @@
|
||||
|
||||
|
||||
# 1、其他可能替代的方案
|
||||
|
||||
## [nalgebra](https://github.com/dimforge/nalgebra)：支持动态数组+数组的计算+数组分解，求解
|
||||
- 1. matrix_construction.rs文件中，nalgebra支持多种矩阵创建方式：
|
||||
|
||||
- 直接指定元素值创建固定大小矩阵（Matrix2x3::new）
|
||||
- 从行向量或列向量创建矩阵（from_rows, from_columns）
|
||||
- 从切片创建矩阵（from_row_slice, from_column_slice）
|
||||
- 使用函数生成矩阵元素（from_fn）
|
||||
- 从迭代器创建矩阵（from_iterator）
|
||||
- 创建动态大小矩阵（DMatrix）
|
||||
- 创建对角矩阵（from_diagonal_element）
|
||||
- 创建单位矩阵（identity）
|
||||
|
||||
- 2. matrix.rs文件，nalgebra支持多种矩阵操作：
|
||||
|
||||
- 矩阵转置（transpose）
|
||||
- 矩阵共轭转置（adjoint）
|
||||
- 矩阵共轭（conjugate）
|
||||
- 矩阵缩放（scale, unscale）
|
||||
- 矩阵元素映射（map, map_with_location）
|
||||
- 矩阵元素折叠（fold, fold_with）
|
||||
- 矩阵元素交换（swap）
|
||||
- 矩阵复制（copy_from, copy_from_slice）
|
||||
- 矩阵迹（trace）
|
||||
- 矩阵对称部分（symmetric_part）
|
||||
- 矩阵厄米特部分（hermitian_part）
|
||||
- 矩阵对角化（diagonal, map_diagonal）
|
||||
- 矩阵齐次坐标转换（to_homogeneous, from_homogeneous）
|
||||
- 矩阵叉积（cross, perp）
|
||||
- 矩阵叉积矩阵（cross_matrix）
|
||||
- 矩阵夹角（angle）
|
||||
|
||||
- 3. src/base/ops.rs文件实现了矩阵的以下主要操作：
|
||||
|
||||
1. 索引操作：
|
||||
|
||||
- 实现了Index和IndexMut trait，支持通过usize或(usize, usize)索引访问矩阵元素
|
||||
- 支持一维和二维索引，会自动进行边界检查
|
||||
|
||||
2. 取反操作：
|
||||
|
||||
- 实现了Neg trait，支持对矩阵进行取反操作
|
||||
- 提供了neg_mut方法用于原地取反
|
||||
|
||||
3. 加法和减法操作：
|
||||
|
||||
- 通过componentwise_binop_impl宏实现了Add/Sub trait和AddAssign/SubAssign trait
|
||||
- 支持矩阵与矩阵、矩阵与标量的加减运算
|
||||
- 提供了add_to/sub_to等方法用于将结果存储到指定矩阵中
|
||||
|
||||
4. 乘法操作：
|
||||
|
||||
- 实现了Mul trait和MulAssign trait
|
||||
- 支持矩阵与矩阵、矩阵与标量的乘法运算
|
||||
- 提供了tr_mul/ad_mul等方法用于转置/共轭转置后的乘法
|
||||
- 实现了Kronecker积运算
|
||||
|
||||
5. 其他操作：
|
||||
|
||||
- 实现了Sum和Product trait，支持对矩阵序列求和或求积
|
||||
- 提供了mul_to等方法用于将结果存储到指定矩阵中
|
||||
|
||||
# 2 本身方法的速度
|
||||
Loading…
x
Reference in New Issue
Block a user