vault backup: 2025-01-24 09:55:06

.obsidian/community-plugins.json

@@ -1,5 +1,6 @@
 [
   "copilot",
   "obsidian-git",
-  "smart-connections"
+  "smart-connections",
+  "obsidian-excalidraw-plugin"
 ]

.obsidian/plugins/obsidian-excalidraw-plugin/data.json

@@ -0,0 +1,789 @@
+{
+  "folder": "Excalidraw",
+  "cropFolder": "",
+  "annotateFolder": "",
+  "embedUseExcalidrawFolder": false,
+  "templateFilePath": "Excalidraw/Template.excalidraw",
+  "scriptFolderPath": "Excalidraw/Scripts",
+  "fontAssetsPath": "Excalidraw/CJK Fonts",
+  "loadChineseFonts": false,
+  "loadJapaneseFonts": false,
+  "loadKoreanFonts": false,
+  "compress": true,
+  "decompressForMDView": false,
+  "onceOffCompressFlagReset": true,
+  "onceOffGPTVersionReset": true,
+  "autosave": true,
+  "autosaveIntervalDesktop": 60000,
+  "autosaveIntervalMobile": 30000,
+  "drawingFilenamePrefix": "Drawing ",
+  "drawingEmbedPrefixWithFilename": true,
+  "drawingFilnameEmbedPostfix": " ",
+  "drawingFilenameDateTime": "YYYY-MM-DD HH.mm.ss",
+  "useExcalidrawExtension": true,
+  "cropPrefix": "cropped_",
+  "annotatePrefix": "annotated_",
+  "annotatePreserveSize": false,
+  "previewImageType": "SVGIMG",
+  "renderingConcurrency": 3,
+  "allowImageCache": true,
+  "allowImageCacheInScene": true,
+  "displayExportedImageIfAvailable": false,
+  "previewMatchObsidianTheme": false,
+  "width": "400",
+  "height": "",
+  "overrideObsidianFontSize": false,
+  "dynamicStyling": "colorful",
+  "isLeftHanded": false,
+  "iframeMatchExcalidrawTheme": true,
+  "matchTheme": false,
+  "matchThemeAlways": false,
+  "matchThemeTrigger": false,
+  "defaultMode": "normal",
+  "defaultPenMode": "never",
+  "penModeDoubleTapEraser": true,
+  "penModeSingleFingerPanning": true,
+  "penModeCrosshairVisible": true,
+  "renderImageInMarkdownReadingMode": false,
+  "renderImageInHoverPreviewForMDNotes": false,
+  "renderImageInMarkdownToPDF": false,
+  "allowPinchZoom": false,
+  "allowWheelZoom": false,
+  "zoomToFitOnOpen": true,
+  "zoomToFitOnResize": true,
+  "zoomToFitMaxLevel": 2,
+  "linkPrefix": "📍",
+  "urlPrefix": "🌐",
+  "parseTODO": false,
+  "todo": "☐",
+  "done": "🗹",
+  "hoverPreviewWithoutCTRL": false,
+  "linkOpacity": 1,
+  "openInAdjacentPane": true,
+  "showSecondOrderLinks": true,
+  "focusOnFileTab": true,
+  "openInMainWorkspace": true,
+  "showLinkBrackets": true,
+  "allowCtrlClick": true,
+  "forceWrap": false,
+  "pageTransclusionCharLimit": 200,
+  "wordWrappingDefault": 0,
+  "removeTransclusionQuoteSigns": true,
+  "iframelyAllowed": true,
+  "pngExportScale": 1,
+  "exportWithTheme": true,
+  "exportWithBackground": true,
+  "exportPaddingSVG": 10,
+  "exportEmbedScene": false,
+  "keepInSync": false,
+  "autoexportSVG": false,
+  "autoexportPNG": false,
+  "autoExportLightAndDark": false,
+  "autoexportExcalidraw": false,
+  "embedType": "excalidraw",
+  "embedMarkdownCommentLinks": true,
+  "embedWikiLink": true,
+  "syncExcalidraw": false,
+  "experimentalFileType": false,
+  "experimentalFileTag": "✏️",
+  "experimentalLivePreview": true,
+  "fadeOutExcalidrawMarkup": false,
+  "loadPropertySuggestions": true,
+  "experimentalEnableFourthFont": false,
+  "experimantalFourthFont": "Virgil",
+  "addDummyTextElement": false,
+  "zoteroCompatibility": false,
+  "fieldSuggester": true,
+  "compatibilityMode": false,
+  "drawingOpenCount": 0,
+  "library": "deprecated",
+  "library2": {
+    "type": "excalidrawlib",
+    "version": 2,
+    "source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.7.5",
+    "libraryItems": []
+  },
+  "imageElementNotice": true,
+  "mdSVGwidth": 500,
+  "mdSVGmaxHeight": 800,
+  "mdFont": "Virgil",
+  "mdFontColor": "Black",
+  "mdBorderColor": "Black",
+  "mdCSS": "",
+  "scriptEngineSettings": {},
+  "defaultTrayMode": true,
+  "previousRelease": "2.7.5",
+  "showReleaseNotes": true,
+  "showNewVersionNotification": true,
+  "latexBoilerplate": "\\color{blue}",
+  "taskboneEnabled": false,
+  "taskboneAPIkey": "",
+  "pinnedScripts": [],
+  "customPens": [
+    {
+      "type": "default",
+      "freedrawOnly": false,
+      "strokeColor": "#000000",
+      "backgroundColor": "transparent",
+      "fillStyle": "hachure",
+      "strokeWidth": 0,
+      "roughness": 0,
+      "penOptions": {
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+        "constantPressure": false,
+        "hasOutline": false,
+        "outlineWidth": 1,
+        "options": {
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+          "smoothing": 0.5,
+          "streamline": 0.5,
+          "easing": "easeOutSine",
+          "start": {
+            "cap": true,
+            "taper": 0,
+            "easing": "linear"
+          },
+          "end": {
+            "cap": true,
+            "taper": 0,
+            "easing": "linear"
+          }
+        }
+      }
+    },
+    {
+      "type": "highlighter",
+      "freedrawOnly": true,
+      "strokeColor": "#FFC47C",
+      "backgroundColor": "#FFC47C",
+      "fillStyle": "solid",
+      "strokeWidth": 2,
+      "roughness": null,
+      "penOptions": {
+        "highlighter": true,
+        "constantPressure": true,
+        "hasOutline": true,
+        "outlineWidth": 4,
+        "options": {
+          "thinning": 1,
+          "smoothing": 0.5,
+          "streamline": 0.5,
+          "easing": "linear",
+          "start": {
+            "taper": 0,
+            "cap": true,
+            "easing": "linear"
+          },
+          "end": {
+            "taper": 0,
+            "cap": true,
+            "easing": "linear"
+          }
+        }
+      }
+    },
+    {
+      "type": "finetip",
+      "freedrawOnly": false,
+      "strokeColor": "#3E6F8D",
+      "backgroundColor": "transparent",
+      "fillStyle": "hachure",
+      "strokeWidth": 0.5,
+      "roughness": 0,
+      "penOptions": {
+        "highlighter": false,
+        "hasOutline": false,
+        "outlineWidth": 1,
+        "constantPressure": true,
+        "options": {
+          "smoothing": 0.4,
+          "thinning": -0.5,
+          "streamline": 0.4,
+          "easing": "linear",
+          "start": {
+            "taper": 5,
+            "cap": false,
+            "easing": "linear"
+          },
+          "end": {
+            "taper": 5,
+            "cap": false,
+            "easing": "linear"
+          }
+        }
+      }
+    },
+    {
+      "type": "fountain",
+      "freedrawOnly": false,
+      "strokeColor": "#000000",
+      "backgroundColor": "transparent",
+      "fillStyle": "hachure",
+      "strokeWidth": 2,
+      "roughness": 0,
+      "penOptions": {
+        "highlighter": false,
+        "constantPressure": false,
+        "hasOutline": false,
+        "outlineWidth": 1,
+        "options": {
+          "smoothing": 0.2,
+          "thinning": 0.6,
+          "streamline": 0.2,
+          "easing": "easeInOutSine",
+          "start": {
+            "taper": 150,
+            "cap": true,
+            "easing": "linear"
+          },
+          "end": {
+            "taper": 1,
+            "cap": true,
+            "easing": "linear"
+          }
+        }
+      }
+    },
+    {
+      "type": "marker",
+      "freedrawOnly": true,
+      "strokeColor": "#B83E3E",
+      "backgroundColor": "#FF7C7C",
+      "fillStyle": "dashed",
+      "strokeWidth": 2,
+      "roughness": 3,
+      "penOptions": {
+        "highlighter": false,
+        "constantPressure": true,
+        "hasOutline": true,
+        "outlineWidth": 4,
+        "options": {
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+          "smoothing": 0.5,
+          "streamline": 0.5,
+          "easing": "linear",
+          "start": {
+            "taper": 0,
+            "cap": true,
+            "easing": "linear"
+          },
+          "end": {
+            "taper": 0,
+            "cap": true,
+            "easing": "linear"
+          }
+        }
+      }
+    },
+    {
+      "type": "thick-thin",
+      "freedrawOnly": true,
+      "strokeColor": "#CECDCC",
+      "backgroundColor": "transparent",
+      "fillStyle": "hachure",
+      "strokeWidth": 0,
+      "roughness": null,
+      "penOptions": {
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+        "outlineWidth": 1,
+        "options": {
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+          "easing": "linear",
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+            "cap": true,
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+          },
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+            "cap": true,
+            "taper": true,
+            "easing": "linear"
+          }
+        }
+      }
+    },
+    {
+      "type": "thin-thick-thin",
+      "freedrawOnly": true,
+      "strokeColor": "#CECDCC",
+      "backgroundColor": "transparent",
+      "fillStyle": "hachure",
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+      "roughness": null,
+      "penOptions": {
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+            "cap": true,
+            "taper": true,
+            "easing": "linear"
+          }
+        }
+      }
+    },
+    {
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+      "strokeColor": "#000000",
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+          }
+        }
+      }
+    },
+    {
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+      "strokeColor": "#000000",
+      "backgroundColor": "transparent",
+      "fillStyle": "hachure",
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+          }
+        }
+      }
+    },
+    {
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+      "strokeColor": "#000000",
+      "backgroundColor": "transparent",
+      "fillStyle": "hachure",
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+      "roughness": 0,
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+            "taper": 0,
+            "easing": "linear"
+          }
+        }
+      }
+    }
+  ],
+  "numberOfCustomPens": 0,
+  "pdfScale": 4,
+  "pdfBorderBox": true,
+  "pdfFrame": false,
+  "pdfGapSize": 20,
+  "pdfGroupPages": false,
+  "pdfLockAfterImport": true,
+  "pdfNumColumns": 1,
+  "pdfNumRows": 1,
+  "pdfDirection": "right",
+  "pdfImportScale": 0.3,
+  "gridSettings": {
+    "DYNAMIC_COLOR": true,
+    "COLOR": "#000000",
+    "OPACITY": 50
+  },
+  "laserSettings": {
+    "DECAY_LENGTH": 50,
+    "DECAY_TIME": 1000,
+    "COLOR": "#ff0000"
+  },
+  "embeddableMarkdownDefaults": {
+    "useObsidianDefaults": false,
+    "backgroundMatchCanvas": false,
+    "backgroundMatchElement": true,
+    "backgroundColor": "#fff",
+    "backgroundOpacity": 60,
+    "borderMatchElement": true,
+    "borderColor": "#fff",
+    "borderOpacity": 0,
+    "filenameVisible": false
+  },
+  "markdownNodeOneClickEditing": false,
+  "canvasImmersiveEmbed": true,
+  "startupScriptPath": "",
+  "openAIAPIToken": "",
+  "openAIDefaultTextModel": "gpt-3.5-turbo-1106",
+  "openAIDefaultVisionModel": "gpt-4o",
+  "openAIDefaultImageGenerationModel": "dall-e-3",
+  "openAIURL": "https://api.openai.com/v1/chat/completions",
+  "openAIImageGenerationURL": "https://api.openai.com/v1/images/generations",
+  "openAIImageEditsURL": "https://api.openai.com/v1/images/edits",
+  "openAIImageVariationURL": "https://api.openai.com/v1/images/variations",
+  "modifierKeyConfig": {
+    "Mac": {
+      "LocalFileDragAction": {
+        "defaultAction": "image-import",
+        "rules": [
+          {
+            "shift": false,
+            "ctrl_cmd": false,
+            "alt_opt": false,
+            "meta_ctrl": false,
+            "result": "image-import"
+          },
+          {
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+            "ctrl_cmd": false,
+            "alt_opt": true,
+            "meta_ctrl": false,
+            "result": "link"
+          },
+          {
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+            "ctrl_cmd": false,
+            "alt_opt": false,
+            "meta_ctrl": false,
+            "result": "image-url"
+          },
+          {
+            "shift": false,
+            "ctrl_cmd": false,
+            "alt_opt": true,
+            "meta_ctrl": false,
+            "result": "embeddable"
+          }
+        ]
+      },
+      "WebBrowserDragAction": {
+        "defaultAction": "image-url",
+        "rules": [
+          {
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+            "meta_ctrl": false,
+            "result": "embeddable"
+          },
+          {
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+            "result": "image-import"
+          }
+        ]
+      },
+      "InternalDragAction": {
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+            "meta_ctrl": true,
+            "result": "embeddable"
+          },
+          {
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+            "result": "image"
+          },
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+            "ctrl_cmd": false,
+            "alt_opt": false,
+            "meta_ctrl": true,
+            "result": "image-fullsize"
+          }
+        ]
+      },
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+        "rules": [
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+            "ctrl_cmd": false,
+            "alt_opt": false,
+            "meta_ctrl": false,
+            "result": "active-pane"
+          },
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+            "ctrl_cmd": true,
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+            "result": "new-tab"
+          },
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+            "ctrl_cmd": true,
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+            "meta_ctrl": false,
+            "result": "new-pane"
+          },
+          {
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+            "ctrl_cmd": true,
+            "alt_opt": true,
+            "meta_ctrl": false,
+            "result": "popout-window"
+          },
+          {
+            "shift": false,
+            "ctrl_cmd": true,
+            "alt_opt": false,
+            "meta_ctrl": true,
+            "result": "md-properties"
+          }
+        ]
+      }
+    },
+    "Win": {
+      "LocalFileDragAction": {
+        "defaultAction": "image-import",
+        "rules": [
+          {
+            "shift": false,
+            "ctrl_cmd": false,
+            "alt_opt": false,
+            "meta_ctrl": false,
+            "result": "image-import"
+          },
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+            "ctrl_cmd": true,
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+            "result": "link"
+          },
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+            "result": "image-url"
+          },
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+            "alt_opt": false,
+            "meta_ctrl": false,
+            "result": "embeddable"
+          }
+        ]
+      },
+      "WebBrowserDragAction": {
+        "defaultAction": "image-url",
+        "rules": [
+          {
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+            "result": "image-url"
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+            "result": "embeddable"
+          },
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+            "alt_opt": false,
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+            "result": "image-import"
+          }
+        ]
+      },
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+        "defaultAction": "link",
+        "rules": [
+          {
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+            "result": "embeddable"
+          },
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+            "result": "image"
+          },
+          {
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+            "ctrl_cmd": true,
+            "alt_opt": true,
+            "meta_ctrl": false,
+            "result": "image-fullsize"
+          }
+        ]
+      },
+      "LinkClickAction": {
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+        "rules": [
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+            "ctrl_cmd": false,
+            "alt_opt": false,
+            "meta_ctrl": false,
+            "result": "active-pane"
+          },
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+            "result": "new-tab"
+          },
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+            "ctrl_cmd": true,
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+            "meta_ctrl": false,
+            "result": "new-pane"
+          },
+          {
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+            "ctrl_cmd": true,
+            "alt_opt": true,
+            "meta_ctrl": false,
+            "result": "popout-window"
+          },
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+            "ctrl_cmd": true,
+            "alt_opt": false,
+            "meta_ctrl": true,
+            "result": "md-properties"
+          }
+        ]
+      }
+    }
+  },
+  "slidingPanesSupport": false,
+  "areaZoomLimit": 1,
+  "longPressDesktop": 500,
+  "longPressMobile": 500,
+  "doubleClickLinkOpenViewMode": true,
+  "isDebugMode": false,
+  "rank": "Bronze",
+  "modifierKeyOverrides": [
+    {
+      "modifiers": [
+        "Mod"
+      ],
+      "key": "Enter"
+    },
+    {
+      "modifiers": [
+        "Mod"
+      ],
+      "key": "k"
+    },
+    {
+      "modifiers": [
+        "Mod"
+      ],
+      "key": "G"
+    }
+  ],
+  "showSplashscreen": true
+}

.obsidian/plugins/obsidian-excalidraw-plugin/manifest.json

@@ -0,0 +1,12 @@
+{
+  "id": "obsidian-excalidraw-plugin",
+  "name": "Excalidraw",
+  "version": "2.7.5",
+  "minAppVersion": "1.1.6",
+  "description": "An Obsidian plugin to edit and view Excalidraw drawings",
+  "author": "Zsolt Viczian",
+  "authorUrl": "https://www.zsolt.blog",
+  "fundingUrl": "https://ko-fi.com/zsolt",
+  "helpUrl": "https://github.com/zsviczian/obsidian-excalidraw-plugin#readme",
+  "isDesktopOnly": false
+}

.obsidian/types.json

@@ -0,0 +1,27 @@
+{
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+    "aliases": "aliases",
+    "cssclasses": "multitext",
+    "tags": "tags",
+    "excalidraw-plugin": "text",
+    "excalidraw-export-transparent": "checkbox",
+    "excalidraw-mask": "checkbox",
+    "excalidraw-export-dark": "checkbox",
+    "excalidraw-export-padding": "number",
+    "excalidraw-export-pngscale": "number",
+    "excalidraw-export-embed-scene": "checkbox",
+    "excalidraw-link-prefix": "text",
+    "excalidraw-url-prefix": "text",
+    "excalidraw-link-brackets": "checkbox",
+    "excalidraw-onload-script": "text",
+    "excalidraw-linkbutton-opacity": "number",
+    "excalidraw-default-mode": "text",
+    "excalidraw-font": "text",
+    "excalidraw-font-color": "text",
+    "excalidraw-border-color": "text",
+    "excalidraw-css": "text",
+    "excalidraw-autoexport": "text",
+    "excalidraw-embeddable-theme": "text",
+    "excalidraw-open-md": "checkbox"
+  }
+}

.obsidian/workspace.json

@@ -4,11 +4,39 @@
     "type": "split",
     "children": [
       {
-        "id": "3b7c67f16ef1a64a",
+        "id": "ec0d65b5f47f4a2a",
         "type": "tabs",
         "children": [
           {
-            "id": "585a4d130ed61c2d",
+            "id": "85d22a0ca1301b67",
+            "type": "leaf",
+            "state": {
+              "type": "markdown",
+              "state": {
+                "file": "多体+耦合求解器/坐标系.md",
+                "mode": "source",
+                "source": false
+              },
+              "icon": "lucide-file",
+              "title": "坐标系"
+            }
+          },
+          {
+            "id": "aa4c94f200dee238",
+            "type": "leaf",
+            "state": {
+              "type": "markdown",
+              "state": {
+                "file": "多体+耦合求解器/计算力和力矩.md",
+                "mode": "source",
+                "source": false
+              },
+              "icon": "lucide-file",
+              "title": "计算力和力矩"
+            }
+          },
+          {
+            "id": "60f9abb64e51146e",
             "type": "leaf",
             "state": {
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@@ -22,21 +50,20 @@
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-            "id": "ed403eb8f95f0215",
+            "id": "0f7e37da67e92e6a",
             "type": "leaf",
             "state": {
-              "type": "split-diff-view",
+              "type": "markdown",
               "state": {
-                "aFile": ".obsidian/workspace.json",
+                "file": "力学书籍/Kane-Dynamics-Theory-Applications/auto/Kane-dynamics-theory翻译.md",
-                "bFile": ".obsidian/workspace.json",
+                "mode": "source",
-                "aRef": ""
+                "source": false
               },
-              "icon": "diff",
+              "icon": "lucide-file",
-              "title": "Diff: workspace.json"
+              "title": "Kane-dynamics-theory翻译"
             }
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-        ],
+        ]
-        "currentTab": 1
       }
     ],
     "direction": "vertical"
@@ -67,7 +94,7 @@
             "state": {
               "type": "search",
               "state": {
-                "query": "",
+                "query": "r_pc",
                 "matchingCase": false,
                 "explainSearch": false,
                 "collapseAll": false,
@@ -92,7 +119,7 @@
       }
     ],
     "direction": "horizontal",
-    "width": 278.5
+    "width": 354.5
   },
   "right": {
     "id": "de2dec4e906755e6",
@@ -108,6 +135,7 @@
             "state": {
               "type": "backlink",
               "state": {
+                "file": "力学书籍/Kane-Dynamics-Theory-Applications/auto/Kane-Dynamics-Theory-Applications.md",
                 "collapseAll": false,
                 "extraContext": false,
                 "sortOrder": "alphabetical",
@@ -117,7 +145,7 @@
                 "unlinkedCollapsed": true
               },
               "icon": "links-coming-in",
-              "title": "反向链接"
+              "title": "Kane-Dynamics-Theory-Applications 的反向链接列表"
             }
           },
           {
@@ -126,11 +154,24 @@
             "state": {
               "type": "outgoing-link",
               "state": {
+                "file": "力学书籍/Kane-Dynamics-Theory-Applications/auto/Kane-Dynamics-Theory-Applications.md",
                 "linksCollapsed": false,
                 "unlinkedCollapsed": true
               },
               "icon": "links-going-out",
-              "title": "出链"
+              "title": "Kane-Dynamics-Theory-Applications 的出链列表"
+            }
+          },
+          {
+            "id": "974d410a4bde10bf",
+            "type": "leaf",
+            "state": {
+              "type": "pdf",
+              "state": {
+                "file": "力学书籍/Kane-Dynamics-Theory-Applications/auto/Kane-Dynamics-Theory-Applications_origin.pdf"
+              },
+              "icon": "lucide-file-text",
+              "title": "Kane-Dynamics-Theory-Applications_origin"
             }
           },
           {
@@ -152,10 +193,10 @@
             "state": {
               "type": "outline",
               "state": {
-                "file": "多体求解器编写/多体+水动 platform+tower debug.md"
+                "file": "力学书籍/FASTLoads/auto/FASTLoads.md"
               },
               "icon": "lucide-list",
-              "title": "多体+水动 platform+tower debug 的大纲"
+              "title": "FASTLoads 的大纲"
             }
           },
           {
@@ -167,13 +208,33 @@
               "icon": "git-pull-request",
               "title": "Source Control"
             }
+          },
+          {
+            "id": "162ba1965655cb5e",
+            "type": "leaf",
+            "state": {
+              "type": "smart-connections-view",
+              "state": {},
+              "icon": "lucide-file",
+              "title": "插件不再活动"
+            }
+          },
+          {
+            "id": "b55183b559c43c96",
+            "type": "leaf",
+            "state": {
+              "type": "copilot-chat-view",
+              "state": {},
+              "icon": "message-square",
+              "title": "Copilot"
+            }
           }
         ],
-        "currentTab": 4
+        "currentTab": 5
       }
     ],
     "direction": "horizontal",
-    "width": 679.5
+    "width": 360.5
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   "left-ribbon": {
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@@ -185,60 +246,62 @@
       "command-palette:打开命令面板": false,
       "copilot:Open Copilot Chat": false,
       "obsidian-git:Open Git source control": false,
+      "obsidian-excalidraw-plugin:新建绘图文件": false,
       "smart-connections:Open: View Smart Connections": false,
       "smart-connections:Open: Smart Chat Conversation": false
     }
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-  "active": "ed403eb8f95f0215",
+  "active": "8080c9209794d082",
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+    "Excalidraw/Drawing 2025-01-20 10.29.17.excalidraw.md",
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 }

Excalidraw/Drawing 2025-01-20 10.29.17.excalidraw.md

@@ -0,0 +1,806 @@
+---
+
+excalidraw-plugin: parsed
+tags: [excalidraw]
+
+---
+==⚠  Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
+
+
+# Excalidraw Data
+
+## Text Elements
+# position ^WGE8EUn2
+
+i = 1-12
+i = 1,  p.dofs.srt_ps[i-1] = 11
+
+srt_ps // Sorted version of PS(), from smallest to largest DOF index
+ps // Array of DOF indices to the active (enabled) DOFs/states
+
+augmat [10, 10]
+
+pmom_bnc_rt: 在基板 (point O) 处由机舱、发电机和转子产生的偏力矩 [-]
+ ^Go680AnZ
+
+## Embedded Files
+aaafbef3a38cbef153740247e445222dcd248461: [[Pasted Image 20250120103502_252.png]]
+
+fbeb81f661da648ae635aabc7ab952254c52421a: [[Pasted Image 20250122185202_369.png]]
+
+%%
+## Drawing
+```compressed-json
+N4KAkARALgngDgUwgLgAQQQDwMYEMA2AlgCYBOuA7hADTgQBuCpAzoQPYB2KqATLZMzYBXUtiRoIACyhQ4zZAHoFAc0JRJQgEYA6bGwC2CgF7N6hbEcK4OCtptbErHALRY8RMpWdx8Q1TdIEfARcZgRmBShcZQUebQB2bQBWGjoghH0EDihmbgBtcDBQMBKIEm4IAAUALQBmav0AcQBpQgAGAE4ASXokiiMAdQoAFgBNAH0qflLYRArCfWikachM
+
+bmdhpOHtAEYktradg54ADk2kneGViBh1gDZ4k+1hnh4Lu53ajp2H2uuKEjqbi1Wo7bRtWpJJInV4vWp3WpXQqQSQIQjKaTcYa1NoJNp3fYwi5JHjxRHXazKYLcNrXZhQUhsADWCAAwmx8GxSBUGdZmHBcIFsqkSpBNLhsEzlIyhBxiOzOdyJLyOPzBVkoCLSgAzQj4fAAZVg1Ikgg8WoEDOZCAGgMk3D4yIg9MZLKNMBN6DN5WuMoxHHCuTQO2ub
+
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+```
+%%

InterestingStuffs/杂项/清洁 Logitech 设备.md

@@ -0,0 +1 @@
+https://support.logi.com/hc/zh-cn/articles/360023416333-%E6%B8%85%E6%B4%81-Logitech-%E8%AE%BE%E5%A4%87

力学书籍/FASTLoads/auto/FASTLoads.md

@@ -687,20 +687,30 @@ Thus, both the load summation method and the constraint method are equivalent.
 
 There are 10 output loads at the tower top / yaw bearing location.  5 of them are the 3 components of tower top force $F_{N a c,R o t}^{o}$ (2 components are expressed in a nonrotating frame, 2 components are expressed in a rotating frame, and 1 component is independent of rotation).  The 5 other loads are the 3 components of the tower top bending moment, $M_{N a c,R o t}^{B@O}$ (again, 2 components are expressed in a nonrotating frame, 2 components are expressed in a rotating frame, and 1 component is independent of rotation).  All these loads are given relative to point O as indicated.  Note that none of these loads include the effects of the yaw bearing mass (YawBrMass), which would affect the forces but not the moments.  The new generalized active force for the equations of motion resulting from these new loads is:  
 
+在塔顶/偏航承载位置有10个输出负载。其中5个是塔顶力的3个分量$F_{N a c,R o t}^{o}$ （2个分量以非旋转框架表示，2个分量以旋转框架表示，1个分量与旋转无关）。另外5个负载是塔顶弯矩的3个分量  $M_{N a c,R o t}^{B@O}$ （同样，2个分量以非旋转框架表示，2个分量以旋转框架表示，1个分量与旋转无关）。所有这些负载相对于点 O 给出。请注意，这些负载不包括偏航承载质量（YawBrMass）的影响，后者会影响力但不影响矩。由于这些新负载导致运动方程中的新广义活动力为：
+
 $$
-F_{r}\big|_{N a c,R o t}={^{E}\nu_{r}^{o}}\cdot F_{N a c,R o t}^{o}+{^{E}\omega_{r}^{B}}\cdot M_{N a c,R o t}^{B@O}\quad\left(r=l,2,...,22\right)
+F_{r}\big|_{N a c,R o t}={^{E}\nu_{r}^{o}}\cdot F_{N a c,R o t}^{o}+{^{E}\omega_{r}^{B}}\cdot M_{N a c,R o t}^{B@O}\quad\left(r=1,2,...,22\right)
 $$  
 
 This generalized active force must produce the same effects as the generalized active and inertia forces associated with everything but the tower and platform.  Thus,  
 
 $$
-\begin{array}{r l}&{\left.F_{r}^{*}\right|_{N}F_{r}^{*}\right|_{R}+F_{r}^{*}\Big|_{G}+F_{r}^{*}\Big|_{H}+F_{r}^{*}\Big|_{B I}+F_{r}^{*}\Big|_{B^{2}}F_{r}^{*}\Big|_{A}}\\ &{+F_{r}\Big|_{A e r o b I}+F_{r}\Big|_{A e r o b2}+F_{r}\Big|_{A e r o a l}+F_{r}\Big|_{G r o w N}+F_{r}\Big|_{G r o w H}+F_{r}\Big|_{G r o w M}+F_{r}\Big|_{G r o w B I}+F_{r}\Big|_{G r o w B2}+F_{r}\Big|_{G r o w B2}}\\ &{+F_{r}\Big|_{S p r i n g Y a w}+F_{r}\Big|_{D a r m p Y a w}+F_{r}\Big|_{S p r i n g R F}+F_{r}\Big|_{D a r m p R F}+F_{r}\Big|_{S p r i n g T e e t}+F_{r}\Big|_{D a r m p T e e t}+F_{r}\Big|_{S p r i n g T e r}+F_{r}\Big|_{S p r i n g T e}+F_{r}\Big|_{H}}\\ &{+F_{r}\Big|_{E l a s t i c B}+F_{r}\Big|_{D a r m p B I}+F_{r}\Big|_{E l a s t i c B2}+F_{r}\Big|_{E l a w p B2}+F_{r}\Big|_{E l a s t i c B\cap r e}+F_{r}\Big|_{D a r m D D r i v e}}\end{array}
+\begin{aligned}
+\left.F_r\right|_{\text {Nac,Rot }}= & \left.\left.F_r^*\right|_N +F_r^*\right|_R+\left.F_r^*\right|_G+\left.F_r^*\right|_H+\left.F_r^*\right|_{\text {B1 }}+\left.\left.F_r^*\right|_{B 2} F_r^*\right|_A \\
+& +\left.F_r\right|_{\text {AeroB1 }}+\left.F_r\right|_{\text {AeroB2 }}+\left.F_r\right|_{\text {AeroA }}+\left.F_r\right|_{\text {GravN }}+\left.F_r\right|_{\text {GravR }}+\left.F_r\right|_{\text {GravH }}+\left.F_r\right|_{\text {GravB1 }}+\left.F_r\right|_{\text {GravB2 }}+\left.F_r\right|_{\text {GravA }}+\left.F_r\right|_{\text {Gen }}+\left.F_r\right|_{\text {Brake }}+\left.F_r\right|_{\text {GBFric }} \quad(r=1,2, \ldots, 22) \\
+& +\left.F_r\right|_{\text {SpringYaw }}+\left.F_r\right|_{\text {DampYaw }}+\left.F_r\right|_{\text {SpringRF }}+\left.F_r\right|_{\text {DampRF }}+\left.F_r\right|_{\text {SpringTeet }}+\left.F_r\right|_{\text {DampTeet }}+\left.F_r\right|_{\text {SpringTF }}+\left.F_r\right|_{\text {DampTF }} \\
+& +\left.F_r\right|_{\text {ElasticB1 }}+\left.F_r\right|_{\text {DampB1 }}+\left.F_r\right|_{\text {ElasticB } 2}+\left.F_r\right|_{\text {DampB } 2}+\left.F_r\right|_{\text {ElasticDrive }}+\left.F_r\right|_{\text {DampDrive }}
+\end{aligned}
 $$  
 
-Since $\varepsilon_{\nu_{r}^{o}}$ and $\varepsilon_{\pmb{\omega}_{r}^{B}}$ are equal to zero unless $r=1,2,...,10$ , the generalized active forces associated with blade, drivetrain, yaw, rotor-furl, tail-furl, and teeter elasticity and damping as well as the generator torque, high-speed shaft braking torque, and gearbox friction do not contribute to the tower top loads (since also, Fr ElasticB1, Fr DampB1, Fr E $\left.\phantom{\frac{1}{\mu_{2}}}\!\!\!,F\right|_{D a m p B2},\left.F\right|_{S p r i n g T e e},\left.F\right|_{D a m p T e e},\left.F\right|_{S p r i n g R F},\left.F\right|_{D a m p R F},\left.F\right|_{S p r i n g T e},\left.F\right|_{D a m p T e},\left.F\right|_{D a m p T e},\left.F\right|_{D a m p T e},\left.F\right|_{P a n p T e}$ SpringYaw, Fr DampYaw, $F_{r}|_{E l a s t i c D r i v e}\,,\;F_{r}|_{D a m p D r i v e}\,,\;F_{r}|_{G e n}\,,\;F_{r}|_{B r a k e}\,;$ , and $F_{r}|_{G B F r i c}$ are equal to zero if $r=1,2,...,10\rangle$ ).  So,  
+Since ${^{E}\nu_{r}^{o}}$ and ${^{E}\omega_{r}^{B}}$ are equal to zero unless $r=1,2,...,10$ , the generalized active forces associated with blade, drivetrain, yaw, rotor-furl, tail-furl, and teeter elasticity and damping as well as the generator torque, high-speed shaft braking torque, and gearbox friction do not contribute to the tower top loads (since also, $F_r^*|_{ElasticB1}, F_r^*|_{DampB1}, F_r^*|_{ElasticB2}$ $\left.\phantom{\frac{1}{\mu_{2}}}\!\!\!,F\right|_{D a m p B2},\left.F\right|_{S p r i n g T e e},\left.F\right|_{D a m p T e e},\left.F\right|_{S p r i n g R F},\left.F\right|_{D a m p R F},\left.F\right|_{S p r i n g T e},\left.F\right|_{D a m p T e},\left.F\right|_{D a m p T e},\left.F\right|_{D a m p T e},\left.F\right|_{P a n p T e}$ SpringYaw, Fr DampYaw, $F_{r}|_{E l a s t i c D r i v e}\,,\;F_{r}|_{D a m p D r i v e}\,,\;F_{r}|_{G e n}\,,\;F_{r}|_{B r a k e}\,;$ , and $F_{r}|_{G B F r i c}$ are equal to zero if $r=1,2,...,10\rangle$ ).  So,  
 
 $$
-\begin{array}{r l}&{\left.F_{r}^{*}\right|_{B I}+F_{r}\right|_{A e r o B I}+F_{r}\big|_{G r a v B I}+F_{r}^{*}\big|_{B I}+F_{r}\big|_{A e r o B2}+F_{r}\big|_{G r a v B2}+F_{r}\big|_{G r a v B2}+F_{r}^{*}\big|_{H}+F_{r}\big|_{G r a v H}+F_{r}^{*}\big|_{R}+F_{r}\big|_{G r a v B}}\\ &{+F_{r}^{*}\big|_{A}+F_{r}\big|_{G r a v A}+F_{r}\big|_{A e r o A}+F_{r}^{*}\big|_{N}+F_{r}\big|_{G r a v N}}\end{array}
+\begin{aligned}
+\left.F_r\right|_{\text {Nac,Rot }} & =\left.F_r^*\right|_{B 1}+\left.F_r\right|_{\text {AeroB1 }}+\left.F_r\right|_{G r a v B 1}+\left.F_r^*\right|_{B 2}+\left.F_r\right|_{\text {AeroB } 2}+\left.F_r\right|_{G r a v B 2}+\left.F_r^*\right|_H+\left.F_r\right|_{G r a v H}+\left.F_r^*\right|_R+\left.F_r\right|_{G r a v R}+\left.F_r^*\right|_G \quad(r=1,2, \ldots, 10) \\
+& +\left.F_r^*\right|_A+\left.F_r\right|_{G r a v A}+\left.F_r\right|_{\text {AeroA }}+\left.F_r^*\right|_N+\left.F_r\right|_{G r a v N}
+\end{aligned}
 $$  
 
 When using the results for the rotor-furl and tail-furl loads, this equation can be simplified as follows:  
@@ -712,97 +722,120 @@ $$
 Thus,  
 
 $$
-{\bf\mu}_{c,R o t}=^{E}\nu_{r}^{V}\cdot F_{G e n,R o t}^{V}+^{E}\omega_{r}^{N}\cdot M_{G e n,R o t}^{N\omega V}+^{E}\nu_{r}^{W}\cdot F_{T a i l}^{W}+^{E}\omega_{r}^{N}\cdot M_{T a i l}^{N\omega W}-m^{N}\nu_{r}^{U}\cdot\left(^{E}a^{U}+g z_{2}^{U}\right)+\nu_{2}^{U}\cdot F_{T a i l}^{W}
+\left.F_r\right|_{\text {Nac,Rot }}={ }^E \boldsymbol{v}_r^V \cdot \boldsymbol{F}_{G e l, R o t}^V+{ }^E \boldsymbol{\omega}_r^N \cdot \boldsymbol{M}_{G e n, \text { Rot }}^{N @ V}+{ }^E \boldsymbol{v}_r^W \cdot \boldsymbol{F}_{\text {Tail }}^W+{ }^E \boldsymbol{\omega}_r^N \cdot \boldsymbol{M}_{\text {Tail }}^{N @ W}-m^{N E} \boldsymbol{v}_r^U \cdot\left({ }^E \boldsymbol{a}^U+g \boldsymbol{z}_2\right)-{ }^E \boldsymbol{\omega}_r^N \cdot\left(\overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\alpha}^N+{ }^E \boldsymbol{\omega}^{\boldsymbol{N}} \times \overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\omega}^{\boldsymbol{N}}\right) \quad(r=1,2, \ldots, 10)
-$$  
-
-$$
-\varepsilon_{\nu_{r}^{W}}\cdot F_{r a i l}^{W}+^{\varepsilon}\omega_{r}^{N}\cdot M_{r a i l}^{N\bar{\alpha}W}-m^{N\;E}\nu_{r}^{U}\cdot\left(^{E}a^{U}+g z_{2}\right)-^{E}\omega_{r}^{N}\cdot\left(\overline{{\boldsymbol{I}}}^{N}\cdot^{E}\alpha^{N}+^{E}\omega^{N}\times\overline{{\boldsymbol{I}}}^{N}\cdot^{E}\boldsymbol{\epsilon}_{\omega}\right).
 $$  
 
+  
 However, $^E\pmb{\omega}_{r}^{N}$ and $^E{\omega}_{r}^{B}$ are all equal when $r$ is constrained to be between 1 and 10.  Thus, when grouping like terms:  
 
 $$
-\cdot F_{\mathit{r a i l}}^{\psi}-m^{^{N}\,^{E}}\nu_{_{r}}^{U}\cdot\left({^{E}a^{U}}+g z_{_{2}}\right)+{^{E}\omega_{_{r}}^{B}}\cdot\left(M_{\mathit{G e n,R o t}}^{\scriptscriptstyle{N}\oplus V}+M_{\mathit{T a i l}}^{\scriptscriptstyle{N}\oplus W}-\overline{{{\overline{{{I}}}}}}\,^{N}\cdot{^{E}a^{N}}-{^{E}\omega^{N}}\times\overline{{{\overline{{{I}}}}}}\,^{N}\cdot{^{E}\omega^{N}}\right)
+\left.F_r\right|_{\text {Nac,Rot }}={ }^E \boldsymbol{v}_r^V \cdot \boldsymbol{F}_{G e n, R o t}^{\boldsymbol{V}}+{ }^E \boldsymbol{v}_r^W \cdot \boldsymbol{F}_{\text {Tail }}^W-m^{N E} \boldsymbol{v}_r^U \cdot\left({ }^E \boldsymbol{a}^U+g z_2\right)+{ }^E \boldsymbol{\omega}_r^B \cdot\left(\boldsymbol{M}_{G e r, R o t}^{N @ V}+\boldsymbol{M}_{\text {Tail }}^{N @ W}-\overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\alpha}^N-{ }^E \boldsymbol{\omega}^N \times \overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\omega}^N\right) \quad(r=1,2, \ldots, 10)
 $$  
 
-Recognizing also that $\begin{array}{r l r l r l r}{^{E}\psi_{r}^{U}=^{E}\psi_{r}^{o}+^{E}\omega_{r}^{B}\times r^{o U}\,,}&{\quad}&{^{E}\psi_{r}^{V}=^{E}\psi_{r}^{o}+^{E}\omega_{r}^{B}\times r^{o V}\,,}&{\quad}&{\mathrm{and}}&{\quad^{E}\psi_{r}^{W}=^{E}\psi_{r}^{O}+^{E}\omega_{r}^{A}\times r^{o V}\,.}\end{array}$ ωrB×rOW ,  when $\begin{array}{r l r}{r}&{{}=}&{1,2,...,10,}\end{array}$ ,  this generalized force can be expanded to:  
+Recognizing also that ${ }^E v_r^U={ }^E v_r^O+{ }^E \omega_r^B \times r^{O U}$ , ${ }^E v_r^V={ }^E v_r^O+{ }^E \omega_r^B \times r^{O V}$ , ${ }^E v_r^W={ }^E v_r^O+{ }^E \omega_r^B \times r^{O W}$, when $\begin{array}{r l r}{r}&{{}=}&{1,2,...,10,}\end{array}$ ,  this generalized force can be expanded to:  
 
 $$
-\begin{array}{l}{{\bf\Pi}_{r}=\Bigl(^{E}\nu_{r}^{o}+^{E}\omega_{r}^{B}\times r^{o\nu}\Bigr)\cdot F_{\epsilon{e n},R o t}^{\gamma}+\Bigl(^{E}\nu_{r}^{o}+^{E}\omega_{r}^{B}\times r^{o\psi}\Bigr)\cdot F_{\epsilon{u i l}}^{\psi}-m^{N}\Bigl(^{E}\nu_{r}^{o}+^{E}\omega_{r}^{B}\times r^{o\psi}\Bigr)\cdot\Bigl(^{E}\nu_{r}^{o}\Bigr)\cdot F_{\epsilon{e n},R o t}^{\gamma}}\\ {{\bf\Pi}_{{\bf\Pi}+}=^{E}\omega_{r}^{B}\cdot\Bigl(M_{G e n,R o t}^{N\bar{\omega}V}+M_{T o l l}^{N\bar{\omega}V}-\overline{{I}}^{N}\cdot^{E}\alpha_{r}^{N}-^{E}\omega_{r}^{N}\times\overline{{I}}^{N}\cdot^{E}\omega^{N}\Bigr)}\end{array}
+\begin{aligned}
+\left.F_r\right|_{\text {Nac, Rot }}= & \left({ }^E \boldsymbol{v}_r^o+{ }^E \boldsymbol{\omega}_r^B \times \boldsymbol{r}^{O \boldsymbol{V}}\right) \cdot \boldsymbol{F}_{\text {Gen,Rot }}^V+\left({ }^E \boldsymbol{v}_r^O+{ }^E \boldsymbol{\omega}_r^B \times \boldsymbol{r}^{O W}\right) \cdot \boldsymbol{F}_{\text {Tail }}^W-m^N\left({ }^E \boldsymbol{v}_r^O+{ }^E \boldsymbol{\omega}_r^B \times \boldsymbol{r}^{O U}\right) \cdot\left({ }^E \boldsymbol{a}^U+g \boldsymbol{z}_2\right) \\
+& +{ }^E \boldsymbol{\omega}_r^B \cdot\left(\boldsymbol{M}_{\text {Gen,Rot }}^{N @ V}+\boldsymbol{M}_{\text {Tail }}^{N @ W}-\overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \alpha^N-{ }^E \boldsymbol{\omega}^N \times \overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\omega}^N\right)
+\end{aligned}
 $$  
 
 Now applying the cyclic permutation law of the scalar triple product:  
 
 $$
-\begin{array}{r l}{\mathrm{~\boldmath~\sigma~}_{r}=}&{{}^{E}\nu_{r}^{o}\cdot\left[F_{G\!e n,R o t}^{V}+F_{r a i l}^{W}-m^{N}\left({\}^{E}a^{U}+g z_{2}\right)\right]+}\\ {\mathrm{~\boldmath~\sigma~}_{+}=}&{{}^{E}\omega_{r}^{B}\cdot\left(M_{G\!e n,R o t}^{N\!\langle~}+M_{T a i l}^{N\!\langle~}-\overline{{{\cal I}}}^{N}\cdot{\}^{E}a^{N}-{\}^{E}\omega^{N}\times\overline{{{\cal I}}}^{N}\cdot{\}^{E}\omega^{N}\right)}\end{array}
+\begin{aligned}
+\left.F_r\right|_{\text {Nac,Rot }}= & { }^E \boldsymbol{v}_r^O \cdot\left[\boldsymbol{F}_{\text {Geln,Rot }}^V+\boldsymbol{F}_{\text {Tail }}^W-m^N\left({ }^E \boldsymbol{a}^U+g \boldsymbol{z}_2\right)\right]+{ }^E \boldsymbol{\omega}_r^B \cdot\left[r^{O \boldsymbol{V}} \times \boldsymbol{F}_{\text {Gel, Rot }}^V+r^{\boldsymbol{OW}} \times \boldsymbol{F}_{\text {Tail }}^W-m^N r^{O U} \times\left({ }^E \boldsymbol{a}^U+g z_2\right)\right] \quad(r=1,2, \ldots, 10) \\
+& +{ }^E \boldsymbol{\omega}_r^B \cdot\left(\boldsymbol{M}_{\text {Geln,Rot }}^{N @ V}+\boldsymbol{M}_{\text {Tail }}^{N @W}-\overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\alpha}^N-{ }^E \boldsymbol{\omega}^N \times \overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\omega}^N\right)
+\end{aligned}
 $$  
 
 which simplifies to:  
 
 $$
-\begin{array}{r l}{\mathit{\Pi}_{\mathit{c},R o t}}&{\overset{\cdot}{=}\varepsilon_{\nu_{r}}^{\bigstar}\cdot\left[F_{\mathit{G e n},R o t}^{V}+F_{\mathit{T a i l}}^{W}-m^{N}\left(\mathit{\Sigma}^{E}a^{U}+g z_{2}\right)\right]}\\ &{\quad\quad+\ ^{E}\omega_{r}^{B}\cdot\left[M_{\mathit{G e n},R o t}^{N\vec{\omega}\gamma}+M_{\mathit{T a i l}}^{N\vec{\omega}W}+r^{O V}\times F_{\mathit{G e n},R o t}^{V}+r^{O W}\times F_{\mathit{T a i l}}^{W}-m^{N}r^{O U}\times\left(\mathit{\Sigma}^{E}a^{U}+g z_{2}\right)-\mathit{\Pi}_{\mathit{c},R o t}^{I}\right]}\end{array}
+\begin{aligned}
+\left.F_r\right|_{\text {Nac, Rot }}= & { }^E \boldsymbol{v}_r^O \cdot\left[\boldsymbol{F}_{\text {Gen,Rot }}^V+\boldsymbol{F}_{\text {Tail }}^W-m^N\left({ }^E \boldsymbol{a}^U+g z_2\right)\right] \\
+& +{ }^E \boldsymbol{\omega}_r^B \cdot\left[\boldsymbol{M}_{\text {Gen,Rot }}^{N @ V}+\boldsymbol{M}_{\text {Tail }}^{N @ W}+\boldsymbol{r}^{O \boldsymbol{V}} \times \boldsymbol{F}_{\text {Gen,Rot }}^V+\boldsymbol{r}^{O\boldsymbol{W}} \times \boldsymbol{F}_{\text {Tail }}^W-m^N r^{O U} \times\left({ }^E \boldsymbol{a}^U+g \boldsymbol{z}_2\right)-\overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\alpha}^N-{ }^E \boldsymbol{\omega}^N \times \overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\omega}^N\right] \quad(r=1,2, \ldots, 10)
+\end{aligned}
 $$  
 
 Thus it is seen that,  
-
+$$
-$M_{N a c,R o t}^{B a O}=M_{G e n,R o t}^{N a V}+M_{T a i l}^{N a V}+r^{o V}\times F_{G e n,R o t}^{V}+r^{o W}\times F_{T a i l}^{W}-m^{N}r^{o U}\times\left(^{E}a^{U}+g z_{2}\right)-\overline{{{\cal I}}}^{N}$ ⋅EαN−EωN×IN⋅EωN  
+\boldsymbol{F}_{\text {Nac,Rot }}^O=\boldsymbol{F}_{\text {Gen,Rot }}^V+\boldsymbol{F}_{\text {Tail }}^W-m^N\left({ }^E \boldsymbol{a}^U+g \boldsymbol{z}_2\right)
+$$
+and 
 
 $$
-F_{_{N a c,R o t}}^{o}=F_{_{G e n,R o t}}^{V}+F_{_{I a i l}}^{W}-m^{N}\left\{\left(\sum_{i=I}^{I I}\varepsilon_{\nu_{i}^{U}}\ddot{q}_{i}\right)\!+\!\left[\sum_{i=J}^{I I}\!\frac{d}{d t}\!\left({^{E}\nu_{i}^{U}}\right)\dot{q}_{i}\right]\!+\!g z_{_{2}}\right\}
+\boldsymbol{M}_{\text {Nac,Rot }}^{B @ O}=\boldsymbol{M}_{G e n, R o t}^{N @ V}+\boldsymbol{M}_{\text {Tail }}^{N @ W}+\boldsymbol{r}^{O V} \times \boldsymbol{F}_{G e n, R o t}^V+\boldsymbol{r}^{O W} \times \boldsymbol{F}_{\text {Tail }}^W-m^N r^{O U} \times\left({ }^E a^U+g z_2\right)-\overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \alpha^N-{ }^E \omega^N \times \overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \omega^N
 $$  
 
-amdMB@O $\begin{array}{l l}{{\displaystyle M_{G e n,R o t}^{N\vec{\omega}V}+M_{T a i l}^{N\vec{\omega}W}+r^{o V}\times F_{G e n,R o t}^{V}+r^{o W}\times F_{T a i l}^{W}-m^{N}r^{o U}\times\left\{\left(\sum_{i=I}^{I I}\varepsilon_{i}^{_V}\ddot{q}_{i}\right)+\left[\sum_{i=I}^{I I}\frac{d}{d t}\Big(^{_E}\nu_{i}^{U}\Big)\right]\right.}}\\ {{\displaystyle\left.-\overline{{{I}}}^{N}\cdot\left\{\left(\sum_{i=I}^{I I}\varepsilon_{o_{i}^{N}}\ddot{q}_{i}\right)+\left[\sum_{i=I}^{I I}\frac{d}{d t}\Big(^{_{E}}\omega_{i}^{N}\Big)\dot{q}_{i}\right]\right\}-^{E}\omega^{N}\times\overline{{{I}}}^{N}\cdot^{E}\omega^{N}}}}\end{array}$ qi+gz2  
+Thus,
+$$
+\boldsymbol{F}_{\text {Nac,Rot }}^o=\boldsymbol{F}_{\text {Gen,Rot }}^{\boldsymbol{V}}+\boldsymbol{F}_{\text {Tail }}^{\boldsymbol{W}}-m^N\left\{\left(\sum_{i=1}^{11}{ }^E \boldsymbol{v}_i^U \ddot{q}_i\right)+\left[\sum_{i=4}^{11} \frac{d}{d t}\left(\boldsymbol{v}^E \boldsymbol{v}_i^U\right) \dot{q}_i\right]+g \boldsymbol{z}_2\right\}
+$$
 
-Or, $\begin{array}{l}{{F_{N a c,R o t_{r}}^{o}=F_{G e n,R o t_{r}}^{V}+F_{T a i l_{r}}^{W}-m^{N^{\textit{E}}}\pmb{\nu}_{r}^{U}\quad\left(r=I,2,...,22\right)}}\\ {{\phantom{=}}}\\ {{F_{N a c,R o t_{t}}^{o}=F_{G e n,R o t_{t}}^{V}+F_{T a i l_{t}}^{W}-m^{N}\left\{\left[\sum_{i=4}^{I I}\frac{d}{d t}\!\left(^{\textit{E}}\nu_{i}^{U}\right)\dot{q}_{i}\right]\!\!+g z_{2}\right\}}}\end{array}$  
+and 
+$$
+\begin{aligned}
+& \boldsymbol{M}_{\text {Nac,Rot }}^{\text {B@O }}=\boldsymbol{M}_{\text {Geln,Rot }}^{N @ V}+\boldsymbol{M}_{\text {Tail }}^{\text {N@W }}+\boldsymbol{r}^{O V} \times \boldsymbol{F}_{\text {Gel, Rot }}^V+\boldsymbol{r}^{OW} \times \boldsymbol{F}_{\text {Tail }}^W-m^N r^{O U} \times\left\{\left(\sum_{i=1}^{11}{ }^E \boldsymbol{v}_i^U \ddot{q}_i\right)+\left[\sum_{i=4}^{11} \frac{d}{d t}\left({ }^E \boldsymbol{v}_i^U\right) \dot{q}_i\right]+g z_2\right\} \\
+& -\overline{\overline{\boldsymbol{I}}}^N \cdot\left\{\left(\sum_{i=4}^{11}{ }^E \boldsymbol{\omega}_j^N \ddot{q}_i\right)+\left[\sum_{i=7}^{11} \frac{d}{d t}\left({ }^E \boldsymbol{\omega}_i^N\right) \dot{q}_i\right]\right\}-{ }^E \boldsymbol{\omega}^N \times \overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\omega}^N
+\end{aligned}
+$$
 
-and 22  
+Or, 
+$$
+\begin{array}{l}{{F_{N a c,R o t_{r}}^{o}=F_{G e n,R o t_{r}}^{V}+F_{T a i l_{r}}^{W}-m^{N^{\textit{E}}}\pmb{\nu}_{r}^{U}\quad\left(r=I,2,...,22\right)}}\\ {{\phantom{=}}}\\ {{F_{N a c,R o t_{t}}^{o}=F_{G e n,R o t_{t}}^{V}+F_{T a i l_{t}}^{W}-m^{N}\left\{\left[\sum_{i=4}^{I I}\frac{d}{d t}\!\left(^{\textit{E}}\nu_{i}^{U}\right)\dot{q}_{i}\right]\!\!+g z_{2}\right\}}}\end{array}
+$$  
+
+and 
+$$
+\boldsymbol{M}_{\text {Nac, Rot }_r}^{B @ O}=\boldsymbol{M}_{G e n, R o t_r}^{\text {N@V }}+\boldsymbol{M}_{\text {Tail }_r}^{N @ W}+\boldsymbol{r}^{O \boldsymbol{V}} \times \boldsymbol{F}_{G e l, R o t_r}^V+\boldsymbol{r}^{O W} \times \boldsymbol{F}_{\text {Tailt}}^W-m^N r^{O U} \times{{ }^E \boldsymbol{v_r}^U} - \overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \omega_r^N\quad\left(r=I,2,...,22\right)
+$$
 
 $$
-\begin{array}{l}{{M_{N a c,R o t_{r}}^{B@O}=M_{G e n,R o t_{r}}^{N@V}+M_{T a l l_{r}}^{N@V}+{r^{o V}}\times F_{G e n,R o t_{r}}^{V}+{r^{o W}}\times F_{T a l l_{r}}^{W}-m^{N}{r^{o U}}\times^{E}\nu_{r}^{U}-\overline{{\overline{{I}}}}^{N}\cdot^{E}\omega,}}\\ {{M_{N a c,R o t_{t}}^{B@O}=M_{G e n,R o t_{t}}^{N@V}+M_{T a l l_{t}}^{N@U}+{r^{o V}}\times F_{G e n,R o t_{t}}^{V}+{r^{o W}}\times F_{T a l l_{t}}^{W}-m^{N}{r^{o U}}\times\left\{\left[\sum_{i=d}^{I I}\frac{d}{d t}\big(^{E}\nu_{i}^{U}\big)\phi_{i}^{2}-m^{N}\right]\right\}.}}\end{array}
+\boldsymbol{M}_{\text {Nac, Rot }_t}^{B @ O}=\boldsymbol{M}_{G e n, R o t_t}^{\text {N@V }}+\boldsymbol{M}_{\text {Tail }_t}^{N @ W}+\boldsymbol{r}^{o \boldsymbol{V}} \times \boldsymbol{F}_{G e l, R o t_t}^V+\boldsymbol{r}^{O W} \times \boldsymbol{F}_{\text {Tailt}}^W-m^N r^{O U} \times\left\{\left[\sum_{i=4}^{I I} \frac{d}{d t}\left({ }^E \boldsymbol{v}_i^U\right) \dot{q}_i\right]+g z_2\right\}-\overline{\overline{\boldsymbol{I}}}^N \cdot\left[\sum_{i=7}^{I I} \frac{d}{d t}\left({ }^E \boldsymbol{\omega}_i^N\right) \dot{q}_i\right]-{ }^E \boldsymbol{\omega}^N \times \overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\omega}^N
 $$  
 
-qi+gz2−IN $\sum_{i=7}^{I I}\frac{d}{d t}\Big(^{E}\pmb{\omega}_{i}^{N}\Big)\dot{q}_{i}$ EωN×I ω  
-
 The output loads are as follows,  
 
-$Y a w B r F x n=F_{N a c,R o t}^{o}\cdot d_{I}\ ⁄I,O O O$   
+$Y a w B r F x n=F_{N a c,R o t}^{o}\cdot d_{1}\ ⁄1000$   Rotating (with nacelle) yaw bearing shear force (directed along the xn-axis), (kN)
-$Y a w B r F y n=-F_{N a c,R o t}^{o}\cdot d_{s}\it{//}\it{I,O O O}$   
+$Y a w B r F y n=-F_{N a c,R o t}^{o}\cdot d_3/1000$   Rotating (with nacelle) yaw bearing shear force (directed along the yn-axis), (kN)
-$Y a w B r F x p=F_{N a c,R o t}^{o}\cdot b_{I}\ensuremath{\,/\,}l,000$   
+$Y a w B r F x p=F_{N a c,R o t}^{o}\cdot b_{1}/1000$   Yaw bearing for-aft (nonrotating) shear force (directed along the xp-axis), (kN) 
-$Y a w B r F y p=-F_{N a c,R o t}^{o}\cdot b_{3}\it{//}\it{I},O O O$   
+$Y a w B r F y p=-F_{N a c,R o t}^{o}\cdot b_{3}/1000$   Yaw bearing side-to-side (nonrotating) shear force (directed along the yp-axis), (kN)
-$Y a w B r F z n=Y a w B r F z p=F_{_{N a c,R o t}}^{o}\cdot d_{_{2}}\ ⁄I,000=F_{_{N a c,R o t}}^{o}\cdot b_{_{2}}⁄I,000$   
+$Y a w B r F z n=Y a w B r F z p=F_{_{N a c,R o t}}^{o}\cdot d_2/1000=F_{_{N a c,R o t}}^{o}\cdot b_2/1000$    Yaw bearing axial force (directed along the zn-/zp-axis), (kN)
-$Y a w B r M x n=M_{N a c,R o t}^{B@O}\cdot d_{I}\ ⁄I,O O O$  
+$Y a w B r M x n=M_{N a c,R o t}^{B@O}\cdot d_1/1000$    Rotating (with nacelle) yaw bearing roll moment (about the xn-axis), $\left(\mathrm{kN}\mathrm{\cdot}\mathrm{m}\right)$  
 
-Rotating (with nacelle) yaw bearing shear force (directed along the xn-axis), (kN) Rotating (with nacelle) yaw bearing shear force (directed along the yn-axis), (kN) Yaw bearing for-aft (nonrotating) shear force (directed along the xp-axis), (kN) Yaw bearing side-to-side (nonrotating) shear force (directed along the yp-axis), (kN) Yaw bearing axial force (directed along the zn-/zp-axis), (kN) Rotating (with nacelle) yaw bearing roll moment (about the xn-axis), $\left(\mathrm{kN}\mathrm{\cdot}\mathrm{m}\right)$  
+ 
 
-$Y a w B r M y n=-M_{\mathit{N a c},\mathit{R o t}}^{\mathit{B@O}}\cdot\mathbf{d_{3}}\left/\mathit{I},000$ $Y a w B r M x p=M_{N a c,R o t}^{B@O}\cdot b_{I}\;/\;I,O O O$ $Y a w B r M y p=-M_{\mathit{N a c},\mathit{R o t}}^{\mathit{B@O}}\cdot b_{3}\mathit{/1},000$  
+$Y a w B r M y n=M_{N a c,R o t}^{B@O}\cdot d_3/1000$ Rotating (with nacelle) yaw bearing pitch moment (about the yn-axis), (kN·m)
+$Y a w B r M x p=M_{N a c,R o t}^{B@O}\cdot b_1/1000$ Nonrotating yaw bearing roll moment (about the xp-axis), (kN·m)
+$Y a w B r M y p=-M_{\mathit{N a c},\mathit{R o t}}^{\mathit{B@O}}\cdot b_{3}/1000$  Nonrotating yaw bearing pitch moment (about the yp-axis), (kN·m)
+$Y a w B r M z n=Y a w B r M z p=M_{N a c,R o t}^{B@O}\cdot d_2/1000=M_{N a c,R o t}^{B@O}\cdot b_2/1000$ Yaw bearing yaw moment (about the zn-/zp-axis), (kN·m)
 
-Rotating (with nacelle) yaw bearing pitch moment (about the yn-axis), $(\mathrm{kN}\!\cdot\!\mathrm{m})$ Nonrotating yaw bearing roll moment (about the xp-axis), $(\mathrm{kN\cdotm})$ Nonrotating yaw bearing pitch moment (about the yp-axis), (kN·m)  
-
-$$
-Y a w B r M z n=Y a w B r M z p=M_{\scriptscriptstyle N a c,R o t}^{\scriptscriptstyle B@O}\cdot d_{\scriptscriptstyle2}\slash{I,00O}=M_{\scriptscriptstyle N a c,R o t}^{\scriptscriptstyle B@O}\cdot b_{\scriptscriptstyle2}\slash{I,00O}
-$$  
-
-Yaw bearing yaw moment (about the zn-/zp-axis), (kN·m)  
 
 Like the LSShftTq, LSSTipMza, RFrlBrM, and TFrlBrM, it is noted that the yaw bearing yaw moment can be computed differently using the yaw drive spring and damper, though the load summation method and this other constraint method are equivalent.  This can be demonstrated as follows. First of all, the equation above is equivalent to saying:  
 
 $$
-\begin{array}{l}{{\imath\nu{\cal B}r{\cal M}z n={}^{E}{\omega}_{Y a w}^{N}\cdot M_{N a c,R a t}^{B@O}\ /\ I,000}}\\ {{\vdots}}\\ {{{\imath\nu{\cal B}r{\cal M}z n={}^{E}{\omega}_{Y a w}^{N}\cdot\bigg[{\cal M}_{G e n,R a t}^{N\ @V}+{\cal M}_{T a i l}^{N\ @V}+{r}^{O V}\times{\cal F}_{G e n,R a t}^{V}+{r}^{O W}\times{\cal F}_{T a i l}^{W}-m^{N}r^{O U}\times\left({}^{E}a^{U}+g e n^{E}a^{U}\right)\bigg]}}\end{array}
+\text { YawBrMzn }={ }^E \omega_{\text {Yaw }}^N \cdot \boldsymbol{M}_{\text {Nac,Rot }}^{B @ O} / 1,000
-$$O Y  
+$$Or,
-
+$$
-)−IN⋅EαN−EωN×IN⋅EωN/ 1,000  
+\text { YawBrMzn }={ }^E \boldsymbol{\omega}_{\text {Yaw }}^N \cdot\left[\boldsymbol{M}_{G e n, \text { Rot }}^{N @ V}+\boldsymbol{M}_{\text {Tail }}^{N @ W}+\boldsymbol{r}^{O V} \times \boldsymbol{F}_{\text {Gen,Rot }}^V+\boldsymbol{r}^{\boldsymbol{O W}} \times \boldsymbol{F}_{\text {Tail }}^{\boldsymbol{W}}-m^N \boldsymbol{r}^{O U} \times\left({ }^E \boldsymbol{a}^U+g \boldsymbol{z}_2\right)-\overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\alpha}^N-{ }^E \boldsymbol{\omega}^N \times \overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\omega}^N\right] / 1,000
+$$
 
 Now applying the cyclic permutation law of the scalar triple product:  
 
 $$
-\imath=\left[\begin{array}{c}{E_{\omega_{Y a w}^{N}}\times r^{O V}\cdot F_{\epsilon\omega,R o n}^{V}+^{E}\omega_{Y a w}^{N}\times r^{O W}\cdot F_{T a i l}^{W}-m^{N\,E}\omega_{Y a w}^{N}\times r^{O U}\cdot\left(^{E}a^{U}+g z_{2}\right)}\\ {+\;^{E}\omega_{Y a w}^{N}\cdot\left(M_{G e n,R o t}^{N\bar{\omega}V}+M_{T a i l}^{N\bar{\omega}W}-\overline{{{I}}}\,^{N}\cdot^{E}a^{N}-^{E}\omega^{N}\times\overline{{{I}}}\,^{N}\cdot^{E}\omega^{N}\right)}\end{array}\right]/\,I,000
+\text { YawBrMzn }=\left[\begin{array}{c}
+{ }^E \boldsymbol{\omega}_{\text {Yaw }}^N \times \boldsymbol{r}^{\boldsymbol{O V}} \cdot \boldsymbol{F}_{\text {Gen,Rot }}^V+{ }^E \boldsymbol{\omega}_{\text {Yaw }}^N \times \boldsymbol{r}^{\boldsymbol{O W}} \cdot \boldsymbol{F}_{\text {Tail }}^W-m^{N E} \boldsymbol{\omega}_{\text {Yaw }}^N \times \boldsymbol{r}^{\boldsymbol{O U}} \cdot\left({ }^E \boldsymbol{a}^U+g \boldsymbol{z}_2\right) \\
++{ }^E \boldsymbol{\omega}_{\text {Yaw }}^N \cdot\left(\boldsymbol{M}_{\text {Gen,Rot }}^{\text {NaV }}+\boldsymbol{M}_{\text {Tail }}^{\text {N@W }}-\overline{\overline{\boldsymbol{I}}}^{\boldsymbol{N}} \cdot{ }^E \boldsymbol{\alpha}^{\boldsymbol{N}}-{ }^E \boldsymbol{\omega}^{\boldsymbol{N}} \times \overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\omega}^N\right)
+\end{array}\right] / 1,000
 $$  
 
 Recognizing also that ${}^{E}{\nu}_{Y a w}^{U}={}^{E}{\omega}_{Y a w}^{N}\times r^{O U}$ ${}^{E}{\nu}_{{\scriptscriptstyle Y a w}}^{V}={}^{E}{\omega}_{{\scriptscriptstyle Y a w}}^{N}\times{r}^{O V}$ and ${}^{E}{\nu}_{Y a w}^{W}={}^{E}{\omega}_{Y a w}^{N}\times r^{O W}$ , this can be expanded as follows:  
 
-$Y a w B r M z n=\Bigg[^{E}\nu_{Y a w}^{V}\cdot F_{\epsilon\epsilon_{n},R o t}^{V}+^{E}\omega_{Y a w}^{N}\cdot M_{G e n,R o t}^{N\vec{\omega}V}+^{E}\nu_{Y a w}^{W}\cdot F_{T a i l}^{W}+^{E}\omega_{Y a w}^{N}\cdot M_{T a i l}^{N\vec{\omega}W}-m^{N}\boldsymbol{\varepsilon}_{V a p}^{W}\cdot\boldsymbol{\nu}_{X a w}^{T}\Bigg]$ vYUaw⋅(EaU+gz2)−EωYNaw⋅(IN⋅EαN+EωN×IN⋅EωN)/ 1,000   
+$\text { YawBrMzn }=\left[{ }^E \boldsymbol{v}_{\text {Yaw }}^V \cdot \boldsymbol{F}_{\text {Gen,Rot }}^V+{ }^E \boldsymbol{\omega}_{\text {Yaw }}^N \cdot \boldsymbol{M}_{\text {Gen,Rot }}^{\text {NaV }}+{ }^E \boldsymbol{v}_{\text {Yaw }}^W \cdot \boldsymbol{F}_{\text {Tail }}^W+{ }^E \boldsymbol{\omega}_{\text {Yaw }}^N \cdot \boldsymbol{M}_{\text {Tail }}^{\text {N@W }}-m^{N{ }^E} \boldsymbol{v}_{\text {Yaw }}^U \cdot\left({ }^E \boldsymbol{a}^{\boldsymbol{U}}+g \boldsymbol{z}_2\right)-{ }^E \boldsymbol{\omega}_{\text {Yaw }}^N \cdot\left(\overline{\overline{\boldsymbol{I}}}^N \cdot{ }^E \boldsymbol{\alpha}^{\boldsymbol{N}}+{ }^E \boldsymbol{\omega}^{\boldsymbol{N}} \times \overline{\overline{\boldsymbol{I}}}^N \cdot{ }^{\boldsymbol{E}} \boldsymbol{\omega}^{\boldsymbol{N}}\right)\right] / 1,000$
 or,   
-$Y a w B r M z n=\left(F_{Y a w}\big|_{R o t o r}+F_{Y a w}\big|_{T a i l}+F_{Y a w}^{*}\big|_{N}+F_{Y a w}\big|_{G r a v N}\right)/\,l,000$  
+$\text { YawBrMzn }=\left(\left.F_{\text {Yaw| }}\right|_{\text {Rotor }}+\left.F_{\text {Yaw }}\right|_{\text {Tail }}+\left.F_{\text {Yaw }}^*\right|_N+\left.F_{\text {Yaw}}\right|_{\text {GravN }}\right) / 1,000$  
 
 $$
 3r M z n=\left(\begin{array}{c}{F_{Y a w}^{*}\Big|_{N}+F_{Y a w}^{*}\Big|_{R}+F_{Y a w}^{*}\Big|_{G}+F_{Y a w}^{*}\Big|_{H}+F_{Y a w}^{*}\Big|_{B I}+F_{Y a w}^{*}\Big|_{B2}+F_{Y a w}^{*}\Big|_{A}+F_{Y a w}^{*}\Big|_{A e r o\theta B I}+F_{Y a w}}\\ {+F_{Y a w}\Big|_{G r a v N}+F_{Y a w}\Big|_{G r a v N}+F_{Y a w}\Big|_{G r a v H}+F_{Y a w}\Big|_{G r a v B I}+F_{Y a w}\Big|_{G r a v B2}+F_{Y a w}\Big|_{G r a v B2}}\end{array}\right)
@@ -811,14 +844,14 @@ $$
 From the equations of motion, it is easily seen that this is equivalent to saying:  
 
 $$
-Y a w B r M z n=\left(-\left.F_{Y a w}\right|_{S p r i n g Y a w}-\left.F_{Y a w}\right|_{D a m p Y a w}\right)/\left.I,000
+\text { YawBrMzn }=\left(-\left.F_{\text {Yav }}\right|_{\text {SpringYav }}-\left.F_{\text {Yav }}\right|_{\text {DampYavv }}\right) / 1,000
 $$  
 
 and thus,  
 
-Y $\iota\boldsymbol{w B r M z n}=\left[Y a w S p r\left(q_{\gamma_{a w}}-Y a w N e u t\right)+Y a w D a m p\cdot\dot{q}_{\gamma_{a w}}\right]/I,000\qquad\qquad(=M_{N a c,R o m p}^{B a o})$ ⋅d2/ 1,000)  
+ $\text { YawBrMzn }=\left[\operatorname{YawSpr}\left(q_{\text {Yaw }}-\operatorname{YawNeut}\right)+\operatorname{YawDamp} \cdot \dot{q}_{\text {Yav }}\right] / 1,000 \quad\left(=\boldsymbol{M}_{\text {Nac,Rot }}^{\text {B@O }} \cdot \boldsymbol{d}_2 / 1,000\right)$ 
 
-Thus, both the load summation method and the constraint method are equivalent.  Thus, to avoid using 2 different methods to calculate YawBrMzn if various DOFs are disabled, it is best just to use $M_{N a c,R o t}^{B@O}\cdot{d_{2}}\,/\,I,O O O$ , which will always work.  
+Thus, both the load summation method and the constraint method are equivalent.  Thus, to avoid using 2 different methods to calculate YawBrMzn if various DOFs are disabled, it is best just to use $\boldsymbol{M}_{\mathrm{Nac}, \mathrm{Rot}}^{\mathrm{B@O}} \cdot \boldsymbol{d}_2 / 1,000$ , which will always work.  
 
 # Tower Base Loads:  
 

多体+耦合求解器/25.1.16思路.canvas

@@ -1,9 +1,9 @@
 {
 	"nodes":[
-		{"id":"4b7faf7953451d56","x":-140,"y":-160,"width":250,"height":60,"type":"text","text":"1、debug转速"},
+		{"id":"4b7faf7953451d56","type":"text","text":"1、debug转速","x":-140,"y":-160,"width":264,"height":60},
-		{"id":"24b6d0ae8c62a4eb","x":-140,"y":-20,"width":250,"height":80,"type":"text","text":"2、Kane原理理解\n- 模态叠加法理解"},
+		{"id":"24b6d0ae8c62a4eb","type":"text","text":"2、Kane原理理解\n- 模态叠加法理解","x":-140,"y":-20,"width":264,"height":80},
-		{"id":"d0a44ee1cb295fda","x":-140,"y":120,"width":250,"height":100,"type":"text","text":"3、增加自由度，对应的广义主动力、惯性力如何推导"},
+		{"id":"d0a44ee1cb295fda","type":"text","text":"3、增加自由度，对应的广义主动力、惯性力如何推导","x":-140,"y":120,"width":264,"height":100},
-		{"id":"e52009c9149e427f","x":160,"y":-160,"width":250,"height":60,"type":"text","text":"模块稳定性"}
+		{"id":"e52009c9149e427f","type":"text","text":"模块稳定性","x":176,"y":-160,"width":264,"height":60}
 	],
 	"edges":[
 		{"id":"2a6d49446576cbc8","fromNode":"4b7faf7953451d56","fromSide":"right","toNode":"e52009c9149e427f","toSide":"left"}

多体+耦合求解器/rust 经验.md

@@ -0,0 +1,21 @@
+
+# array2 debug
+![[Pasted image 20250123103518.png]]
+
+aug_mat矩阵大小600
+
+0，12-24 表示矩阵第0行，12-24列数据
+
+例：
+```rust
+    let matrix: Array2<f64> = array![
+
+        [1.0, 2.0, 3.0],
+
+        [4.0, 5.0, 6.0],
+
+        [7.0, 8.0, 9.0]
+
+    ];
+```
+![[Pasted image 20250123103848.png]]

多体+耦合求解器/yaw.md

@@ -0,0 +1,13 @@
+
+机舱偏航  
+FAST 可以通过将 YawDOF 设置为 True 并将偏航弹簧常数（YawSpr）和偏航阻尼常数（YawDamp）设为零来模拟机舱偏航作为一个完美的铰链，没有抗力。您还可以通过将 YawDamp 设置为非零值来模拟具有偏航阻尼的自由偏航装置。
+
+对于指令偏航位置保持不变的偏航驱动涡轮机，可以通过将 YawDOF 设置为 True、YCMode 设置为 0，并将 YawSpr 和 YawDamp 设为非零值来模拟偏航驱动装置中的柔性和阻尼。FAST 将使用输入参数 YawNeut 作为中性偏航位置（即恒定偏航指令），NacYaw 作为初始偏航角度。在这种情况下，通过偏航承载传递的力矩 YawMom 是：
+$$
+\text{YawMom} = \text{YawSpr} \cdot (\text{YawPos} - \text{YawNeut}) + \text{YawDamp} \cdot \text{YawRate} 
+$$
+其中 YawPos 为即时偏航位置。
+
+对于固定偏航模拟，将 YawDOF 设置为 False、YCMode 设置为 0、TYawManS 大于 TMax，并将 NacYaw 设为固定机舱偏航角度。
+
+您还可以在仿真过程中主动控制机舱偏航运动。有关主动偏航控制选项的信息，请参阅控制章节中的“机舱偏航控制”部分。

多体+耦合求解器/坐标系.md

@@ -0,0 +1,260 @@
+# 惯性坐标系 （xi yi zi）
+- Origin The point about which the translational motions of the support platform (surge,
+sway, and heave) are defined.
+- xi axis Pointing in the nominal (0°) downwind direction.
+- yi axis Pointing to the left when looking in the nominal downwind direction.
+- zi axis Pointing vertically upward opposite to gravity.
+- 平台不运动时与xt yt zt相同
+![[Pasted image 20250120111003.png]]
+
+## 代码中
+z1 = xi
+z2 = zi
+z3 = -yi
+![[Pasted image 20250120111631.png]]
+
+```rust
+    coord_sys.z1 = Array1::from_vec(vec![1.0, 0.0, 0.0]); //Vector / direction z1 (=  xi from the IEC coord. system).
+
+    coord_sys.z2 = Array1::from_vec(vec![0.0, 1.0, 0.0]); //Vector / direction z2 (=  zi from the IEC coord. system).
+
+    coord_sys.z3 = Array1::from_vec(vec![0.0, 0.0, 1.0]); //Vector / direction z3 (= -yi from the IEC coord. system).
+```
+
+# tower base/platform 坐标系
+
+Origin Intersection of the center of the tower and the tower base connection to the support platform.
+xt axis When the support platform has no pitch or yaw displacement, it is aligned with the xi axis (pointing horizontally in the nominal downwind direction).
+yt axis When the support platform has no roll or yaw displacement, it is aligned with the yi axis (pointing to the left when looking in the nominal downwind direction).
+zt axis Pointing up from the center of the tower.
+
+![[Pasted image 20250120111003.png]]
+
+## 代码中
+
+a1 = xt
+a2 = zt
+a3 = -yt
+
+```rust
+    coord_sys.a1 = trans_mat[[0, 0]] * &coord_sys.z1 + trans_mat[[0, 1]] * &coord_sys.z2 + trans_mat[[0, 2]]  * &coord_sys.z3; // Vector / direction a1 (=  xt from the IEC coord. system).
+
+    coord_sys.a2 = trans_mat[[1, 0]] * &coord_sys.z1 + trans_mat[[1, 1]] * &coord_sys.z2 + trans_mat[[1, 2]]  * &coord_sys.z3; // Vector / direction a2 (=  zt from the IEC coord. system).
+
+    coord_sys.a3 = trans_mat[[2, 0]] * &coord_sys.z1 + trans_mat[[2, 1]] * &coord_sys.z2 + trans_mat[[2, 2]]  * &coord_sys.z3; // Vector / direction a3 (= -yt from the IEC coord. system).
+```
+
+# 塔架节点坐标系
+t1 t2 t3**基于a1 a2 a3 加上塔架节点变形角度** 计算得到
+
+# Tower-top/base-plate
+![[Pasted image 20250120112122.png]]
+
+加上塔顶变形
+
+Origin A point on the yaw axis at a height of TowerHt above ground level [onshore or
+mean sea level [offshore] (see Figure 14(a), Figure 16, or Figure 20).
+xp axis When the tower is not deflected, it is aligned with the xt axis.
+yp axis When the tower is not deflected, it is aligned with the yt axis.
+zp axis When the tower is not deflected, it is aligned with the zt axis. It is also the yaw axis.
+
+## 代码中
+b1 = xp
+b2 = zp
+b3 = -yp
+
+
+# Nacelle/Yaw Coordinate System
+
+在p坐标系基础上加变桨角度
+![[Pasted image 20250120141307.png]]
+
+This coordinate system translates and rotates with the top of the tower, plus it yaws with the nacelle.
+Origin The origin is the same as that for the tower-top/base-plate coordinate system.
+xn axis Pointing horizontally toward the nominally downwind end of the nacelle.
+yn axis Pointing to the left when looking toward the nominally downwind end of the nacelle. 
+zn axis Coaxial with the tower/yaw axis and pointing up.
+
+## 代码中
+d1 = xn
+d2 = zn
+d3 = -yn
+
+```rust
+    // Nacelle / yaw coordinate system:
+
+    c_nac_yaw = (x.qt[DOF_YAW as usize - 1]).cos();
+
+    s_nac_yaw = (x.qt[DOF_YAW as usize - 1]).sin();
+
+  
+
+    coord_sys.d1 = c_nac_yaw * &coord_sys.b1 - s_nac_yaw* &coord_sys.b3; // Vector / direction d1 (=  xn from the IEC coord. system).
+
+    coord_sys.d2 = coord_sys.b2.clone();                                        // Vector / direction d2 (=  xn from the IEC coord. system).
+
+    coord_sys.d3 = s_nac_yaw * &coord_sys.b1 + c_nac_yaw* &coord_sys.b3; // Vector / direction d3 (=  xn from the IEC coord. system).
+```
+
+# rotor-furl 坐标系 后续删掉
+
+
+# 主轴坐标系 Shaft Coordinate System
+The shaft coordinate system does not rotate with the rotor, but it does translate and rotate with the tower and it yaws with the nacelle and furls with the rotor.
+The nacelle inertial measurement unit uses this coordinate system for all of its motion outputs. Shaft bending moments at the hub and at the position denoted by ShftGagL use this coordinate system or the rotating hub coordinate system shown below.
+
+机舱惯性、主轴弯曲 tilt
+
+![[Pasted image 20250120141352.png]]
+
+Origin Intersection of the yn-/zn-plane and the rotor axis.
+xs axis Pointing along the (possibly tilted) shaft in the nominally downwind direction.
+ys axis Pointing to the left when looking from the tower toward the nominally downwind end of the nacelle. 
+zs axis Orthogonal with the xs and ys axes such that they form a right-handed coordinate system.
+
+c1=xs
+c2=zs
+c3=-ys
+
+# 方位角坐标系统 azimuth coordinate system
+
+e1 e2 e3
+
+The azimuth, or a, coordinate system is located **at the origin of the shaft coordinate system**, but it rotates with the rotor. When Blade 1 points up, the azimuth and shaft coordinate systems are parallel. For three bladed rotors, blade 3 is ahead of blade 2, which is ahead of blade 1, so that the order of blades passing through a given azimuth is 3-2-1-repeat.
+方位角坐标系（或称为“a”坐标系）位于**主轴坐标系的原点，但随着转子旋转而旋转****。当叶片1指向上方时，方位角和轴坐标系是平行的。对于三叶转子，叶片3在叶片2之前，叶片2在叶片1之前，因此通过给定方位角的叶片顺序为3-2-1-重复。
+
+e1 e2 e3在c1 c2 c3的基础上，加上 DOF_DRTR DOF_GEAZ的角度
+```rust
+// 方位角坐标系统 azimuth coordinate system
+
+c_azimuth = (x.qt[DOF_DRTR as usize - 1] + x.qt[DOF_GEAZ as usize -1]).cos();
+
+s_azimuth = (x.qt[DOF_DRTR as usize - 1] + x.qt[DOF_GEAZ as usize -1]).sin();
+
+
+
+coord_sys.e1 = coord_sys.c1.clone();  // Vector / direction e1 (equivalent to xa from the IEC coordinate system)
+
+
+
+coord_sys.e2 = c_azimuth * &coord_sys.c2 + s_azimuth * &coord_sys.c3;  // Vector / direction e2 (equivalent to ya from the IEC coordinate system)
+
+
+
+coord_sys.e3 = -s_azimuth * &coord_sys.c2 + c_azimuth * &coord_sys.c3;  // Vector / direction e3 (equivalent to za from the IEC coordinate system)
+```
+
+# teeter 坐标系 用于两叶片 后续可以删掉 
+f1=e1
+f2 = e2
+f3 = e3
+
+# hub / delta-3 coordinate system:
+
+The hub coordinate system **rotates with the rotor.** It also teeters in two-bladed models.
+**Origin Intersection of the rotor axis and the plane of rotation (non-coned rotors) or the apex of the cone of rotation (coned rotors).** 
+原点在轮毂
+xh axis Pointing along the hub centerline in the nominal downwind direction.
+yh axis Orthogonal with the xh and zh axes such that they form a right-handed coordinate system. 
+zh axis Perpendicular to the hub centerline with the same azimuth as Blade 1.
+
+![[Pasted image 20250120142238.png]]
+
+g1 = xh
+g2 = yh
+g3 = zh
+**这里变了，不再是2对应z方向**
+
+默认 cos_del3 = 1.0， sin_del3=0.0
+g1 = f1
+g2 = f2
+g3 = f3
+```rust 
+// Hub / delta-3 coordinate system:
+
+    coord_sys.g1 = coord_sys.f1.clone();                                            // Vector / direction g1 (= xh from the IEC coord. system)
+
+    coord_sys.g2 = p.cos_del3 * &coord_sys.f2 + p.sin_del3 * &coord_sys.f3;  // Vector / direction g2 (= yh from the IEC coord. system)
+
+    coord_sys.g3 = -p.sin_del3 * &coord_sys.f2 + p.cos_del3 * &coord_sys.f3; // Vector / direction g3 (= zh from the IEC coord. system)
+```
+
+
+# 锥角坐标系 Coned Coordinate Systems
+i1 i2 i3
+
+There is a coned coordinate system for each blade that rotates with the rotor. The coordinate system does not pitch with the blades and it also teeters in two bladed models. For three-bladed rotors, blade 3 is ahead of blade 2, which is ahead of blade 1, so that the order of blades passing through a given azimuth is 3-2- 1-repeat.
+Origin The origin is the same as that for the hub coordinate system.
+Xc,i axis Orthogonal with the yc,i and zc,i axes such that they form a right-handed coordinate system. (i = 1, 2, or 3 for blades 1, 2, or 3, respectively)
+Yc,i axis Pointing towards the trailing edge of blade i if the pitch and twist were zero and parallel with the chord line. (i = 1, 2, or 3 for blades 1, 2, or 3, respectively)
+Zc,i axis Pointing along the pitch axis towards the tip of blade i. (i = 1, 2, or 3 for blades 1, 2, or 3, respectively)
+
+加入锥角，原点与hub坐标系相同 三个叶片，有三组
+
+i1[k, ..] = xck
+i2[k, ..] = yck
+i3[k, ..] = zck
+![[Pasted image 20250120144724.png]]
+先把轮毂坐标系根据方位角，变换到每个叶片，再处理锥角
+
+```rust
+    for k in 0..p.num_bl as usize{
+
+  
+
+        g_rot_ang = p.two_pi_nb * (k as f64);
+
+        c_g_rot_ang = g_rot_ang.cos();
+
+        s_g_rot_ang = g_rot_ang.sin();
+
+  
+
+        g1_prime = coord_sys.g1.clone();
+
+        g2_prime = c_g_rot_ang * &coord_sys.g2 + s_g_rot_ang * &coord_sys.g3;
+
+        g3_prime = -s_g_rot_ang * &coord_sys.g2 + c_g_rot_ang * &coord_sys.g3;
+
+  
+
+        // coned coordinate system
+
+  
+
+        coord_sys.i1.slice_mut(s![k, ..]).assign(&(p.cos_pre_c[k] * &g1_prime - p.sin_pre_c[k] * &g3_prime)); // i1(K,:) = vector / direction i1 for blade K (=  xcK from the IEC coord. system).
+
+        coord_sys.i2.slice_mut(s![k, ..]).assign(&(g2_prime.clone()));  // i2(K,:) = vector / direction i2 for blade K (=  ycK from the IEC coord. system).
+
+        coord_sys.i3.slice_mut(s![k, ..]).assign(&(p.sin_pre_c[k] * &g1_prime + p.cos_pre_c[k] * &g3_prime)); // i3(K,:) = vector / direction i3 for blade K (=  zcK from the IEC coord. system).
+}
+```
+
+# 叶片坐标系 Blade Coordinate Systems
+
+j1 j2 j3 
+
+These coordinate systems are the same as the coned coordinate systems, except that they pitch with the blades and their origins are at the blade root. For three-bladed rotors, blade 3 is ahead of blade 2, which is ahead of blade 1, so that the order of blades passing through a given azimuth is 3-2-1-repeat.
+
+Origin Intersection of the blade’s pitch axis and the blade root. xb,i axis Orthogonal with the yb and zb axes such that they form a right-handed coordinate system. (i = 1, 2, or 3 for blades 1, 2, or 3, respectively)
+yb,i axis Pointing towards the trailing edge of blade i and parallel with the chord line at the zero-twist blade station. (i = 1, 2, or 3 for blades 1, 2, or 3, respectively)
+zb,i axis Pointing along the pitch axis towards the tip of blade i. (i = 1, 2, or 3 for blades 1, 2, or 3, respectively)
+原点位于叶根，在锥角坐标系基础上加入变桨角
+
+
+j1[k, ..] = xbk
+j2[k, ..] = ybk
+j3[k, ..] = zbk
+![[Pasted image 20250120155301.png]]
+# 叶素节点坐标系
+n1 n2 n3
+m1 m2 m3 不包含叶根 叶尖节点
+
+## 问题：
+- p.c_theta_s 
+- p.s_theta_s 
+- p.twisted_sf是什么
+- n1 n2 n3的计算公式
+- m1 m2 m3的意义
+
+# tail-furl 坐标系统 删掉

多体+耦合求解器/填充augmat.md

@@ -0,0 +1,83 @@
+# yaw
+
+p.dofs.ptte // Array of tower DOF indices contributing to QD2T-related linear accelerations of the tower nodes (point T) 
+npte 塔架 Number of DOFs contributing to QD2T-related linear accelerations of the tower nodes (point T) 计数漂浮式基础自由度+塔架自由度
+
+nptte // Number of **tower DOFs** contributing to QD2T-related linear accelerations of the tower nodes (point T)
+
+
+```rust
+    for l in 0..p.dofs.nptte as usize{
+
+        // Loop through all active (enabled) tower DOFs that contribute to the QD2T-related linear accelerations of the yaw bearing (point O)
+
+        for i in l..p.dofs.nptte as usize{
+
+            // Loop through all active (enabled) tower DOFs greater than or equal to L
+
+            //   [C(q,t)]T of YawBrMass
+
+            aug_mat[[p.dofs.ptte[i] as usize - 1, p.dofs.ptte[l] as usize - 1]] = p.yaw_br_mass *
+
+                                                                    dot_product(&rt_hs.plin_vel_eo.slice(s![p.dofs.ptte[i] as usize -1, 0, ..]).to_owned(),
+
+                                                                                &rt_hs.plin_vel_eo.slice(s![p.dofs.ptte[l] as usize -1, 0, ..]).to_owned());
+
+            // println!("{}",aug_mat[[p.dofs.ptte[i] as usize - 1, p.dofs.ptte[l] as usize - 1]]);
+
+            // println!("{}",p.dofs.ptte[i]);
+
+            // println!("{}",p.dofs.ptte[l]);
+
+        }
+
+    }
+
+    tmpvec1 = -p.yaw_br_mass * (p.gravity * coord_sys.z2.clone() + rt_hs.lin_acc_eot.clone());
+
+    for i in 0..p.dofs.nptte as usize{
+
+        // {-f(qd,q,t)}T + {-f(qd,q,t)}GravT of YawBrMass
+
+  
+
+        aug_mat[[p.dofs.ptte[i] as usize - 1, p.naug as usize - 1]] = dot_product(&rt_hs.plin_vel_eo.slice(s![p.dofs.ptte[i] as usize -1, 0, ..]).to_owned(), &tmpvec1);
+
+        // println!("{}",aug_mat[[p.dofs.ptte[i] as usize - 1, p.naug as usize - 1]]);
+
+        // println!("{}",p.dofs.ptte[i]);
+
+    }
+```
+
+
+p.dofs.diag Array containing indices of SrtPS() associated with each enabled DOF
+srt_ps // Sorted version of PS(), from smallest to largest DOF index
+ps // Array of DOF indices to the active (enabled) DOFs/states
+```rust
+    if p.dof_flag.as_mut().unwrap()[DOF_YAW as usize - 1]{
+
+        for i in p.dofs.diag[DOF_YAW as usize -1]..=p.dofs.n_actv_dof{
+
+            // [C(q,t)]N + [C(q,t)]R + [C(q,t)]G + [C(q,t)]H + [C(q,t)]B + [C(q,t)]A
+
+            aug_mat[[p.dofs.srt_ps[i as usize -1] as usize-1, DOF_YAW as usize-1]] = -1. * dot_product(&rt_hs.p_ang_vel_en.slice(s![DOF_YAW -1, 0, ..]).to_owned(),
+
+                                                                                        &rt_hs.pmom_bnc_rt.slice(s![.., p.dofs.srt_ps[i as usize -1] -1]).to_owned());
+
+            // println!("{}", aug_mat[[p.dofs.srt_ps[i as usize -1] as usize-1, DOF_YAW as usize-1]]);
+
+        }
+
+        // {-f(qd,q,t)}N + {-f(qd,q,t)}GravN + {-f(qd,q,t)}R + {-f(qd,q,t)}GravR + {-f(qd,q,t)}G + {-f(qd,q,t)}H + {-f(qd,q,t)}GravH + {-f(qd,q,t)}B + {-f(qd,q,t)}GravB + {-f(qd,q,t)}AeroB + {-f(qd,q,t)}A + {-f(qd,q,t)}GravA + {-f(qd,q,t)}AeroA
+
+        // + {-f(qd,q,t)}SpringYaw  + {-f(qd,q,t)}DampYaw; NOTE: The neutral yaw rate, YawRateNeut, defaults to zero.  It is only used for yaw control.
+
+        aug_mat[[DOF_YAW as usize-1, p.naug as usize -1]] = dot_product(&rt_hs.p_ang_vel_en.slice(s![DOF_YAW -1, 0, ..]).to_owned(),
+
+                                                            &rt_hs.mom_bnc_rtt) + u.yaw_mom;
+
+        // println!("{}", aug_mat[[DOF_YAW as usize-1, p.naug as usize -1]]);
+
+    }
+```

多体+耦合求解器/理论框架.canvas

@@ -3,14 +3,26 @@
 		{"id":"9461f7dd96103316","type":"text","text":"Kane方法","x":-120,"y":-280,"width":250,"height":50},
 		{"id":"0c8534c8ba68c9a6","type":"text","text":"**广义**主动力","x":-280,"y":-140,"width":250,"height":50},
 		{"id":"5eaa425c204bf600","type":"text","text":"**广义**惯性力","x":40,"y":-140,"width":250,"height":50},
-		{"id":"7351d2bbb065d539","type":"text","text":"动力学 ","x":-210,"y":40,"width":250,"height":60},
 		{"id":"e398416e55019686","type":"text","text":"运动学","x":-210,"y":220,"width":250,"height":60},
 		{"id":"38d3d1a313c094ee","type":"text","text":"广义坐标","x":-280,"y":340,"width":250,"height":60},
-		{"id":"8ec17237cebe7433","type":"text","text":"广义速率","x":60,"y":340,"width":250,"height":60}
+		{"id":"8ec17237cebe7433","type":"text","text":"广义速率","x":60,"y":340,"width":250,"height":60},
+		{"id":"c20eeff7484d8a39","type":"text","text":"叠加法","x":185,"y":140,"width":250,"height":60},
+		{"id":"a729b7930412f0b1","type":"text","text":"需要保持边界条件一致","x":520,"y":140,"width":250,"height":60},
+		{"id":"d405163cb9ecd804","type":"text","text":"叶片多段拆分，小段做模态叠加？","x":520,"y":250,"width":250,"height":60},
+		{"id":"7351d2bbb065d539","type":"text","text":"动力学 ","x":-210,"y":110,"width":250,"height":60},
+		{"id":"da500b2b12ed0901","x":290,"y":-30,"width":250,"height":60,"type":"text","text":"填充augmat矩阵"},
+		{"id":"20ce8d75f0f35588","x":580,"y":-30,"width":250,"height":60,"type":"text","text":"解出来q"},
+		{"id":"6094c53caf966263","x":-165,"y":-40,"width":340,"height":80,"type":"text","text":"由F + F^* 的形式转换到 [C(q,t)]，{-f(qd,q,t)}形式"}
 	],
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 		{"id":"647c1b45edc92b02","fromNode":"9461f7dd96103316","fromSide":"bottom","toNode":"0c8534c8ba68c9a6","toSide":"top"},
 		{"id":"e3d4293dd3262f2d","fromNode":"9461f7dd96103316","fromSide":"bottom","toNode":"5eaa425c204bf600","toSide":"top"},
-		{"id":"9a803fcaec81414e","fromNode":"38d3d1a313c094ee","fromSide":"right","toNode":"8ec17237cebe7433","toSide":"left"}
+		{"id":"9a803fcaec81414e","fromNode":"38d3d1a313c094ee","fromSide":"right","toNode":"8ec17237cebe7433","toSide":"left"},
+		{"id":"7ff52c30a0b0347d","fromNode":"a729b7930412f0b1","fromSide":"bottom","toNode":"d405163cb9ecd804","toSide":"top"},
+		{"id":"d97ef554530b15b5","fromNode":"c20eeff7484d8a39","fromSide":"right","toNode":"a729b7930412f0b1","toSide":"left"},
+		{"id":"034d145edd7cfce0","fromNode":"0c8534c8ba68c9a6","fromSide":"bottom","toNode":"6094c53caf966263","toSide":"top"},
+		{"id":"da18b7fa4859fa6f","fromNode":"5eaa425c204bf600","fromSide":"bottom","toNode":"6094c53caf966263","toSide":"top"},
+		{"id":"5d5f4fef281a656e","fromNode":"6094c53caf966263","fromSide":"right","toNode":"da500b2b12ed0901","toSide":"left"},
+		{"id":"5573fa12a3a02ee0","fromNode":"da500b2b12ed0901","fromSide":"right","toNode":"20ce8d75f0f35588","toSide":"left"}
 	]
 }

多体+耦合求解器/计算position.md

@@ -0,0 +1,34 @@
+
+rz Position vector from inertia frame origin to platform reference (point Z).
+r_zy Position vector from platform reference (point Z) to platform mass center (point Y) [m]
+r_zt0 Position vector from platform reference (point Z) to tower base (point T(0)) [m]
+r_zo Position vector from platform reference (point Z) to tower-top / base plate (point O) [m]
+
+r_ou Position vector from tower-top / base plate (point O) to nacelle center of mass (point U) [m]
+r_ov Position vector from tower-top / base plate (point O) to specified point on rotor-furl axis (point V) [m]
+r_vimu Position vector from specified point on rotor-furl axis (point V) to nacelle IMU (point IMU) [m]
+r_vd Position vector from specified point on rotor-furl axis (point V) to center of mass of structure that furls with the rotor (point D) [m]
+r_vp Position vector from specified point on rotor-furl axis (point V) to teeter pin (point P) [m]
+
+r_pq Position vector from teeter pin (point P) to apex of rotation (point Q) [m]
+r_qc Position vector from apex of rotation (point Q) to hub center of mass (point C) [m]
+r_ow Position vector from tower-top / base plate (point O) to specified point on tail-furl axis (point W) [m]
+r_wi Position vector from specified point on tail-furl axis (point W) to tail boom center of mass (point I) [m]
+r_wj Position vector from specified point on tail-furl axis (point W) to tail fin center of mass (point J) [m]
+r_pc Position vector from teeter pin (point P) to hub center of mass (point C) [m]
+r_t0o Position vector from the tower base (point T(0)) to tower-top / base plate (point O) [m]
+r_o Position vector from inertial frame origin to tower-top / base plate (point O) [m]
+r_v Position vector from inertial frame origin to specified point on rotor-furl axis (point V) [m]
+r_p Position vector from inertial frame origin to teeter pin (point P) [m]
+r_q Position vector from inertial frame origin to apex of rotation (point Q) [m]
+r_j Position vector from inertial frame origin to tail fin center of mass (point J) [m]
+
+r_s0s Position vector from the blade root (point S(0)) to a point on a blade (point S) [m]
+r_qs Position vector from the apex of rotation (point Q) to a point on a blade (point S) [m]
+r_s Position vector from inertial frame origin to a point on a blade (point S) [m]
+r_ps0 Position vector from teeter pin (point P) to blade root (point S(0)) [m]
+
+
+r_zt Position vector from platform reference (point Z) to a point on a tower (point T) [m]
+r_t0t Position vector from a height of TowerBsHt (point T(0)) to a point on the tower (point T) [m]
+r_t Position vector from inertial frame origin to the current node (point T(HNodes(J)) [m]

多体+耦合求解器/计算力和力矩.md

@@ -0,0 +1,59 @@
+# yaw
+
+
+pfrc_oncrt: Partial force at the yaw bearing (point O) due to the nacelle, generator, and rotor [-]
+pmom_bnc_rt: 在基板 (point O) 处由机舱、发电机和转子产生的偏力矩 [-]
+
+```rust
+//  Partial force at the yaw bearing (point O) due to the nacelle, generator, and rotor [-]
+
+    rt_hs.pfrc_oncrt = rt_hs.pfrc_vgn_rt.clone() + rt_hs.pfrc_wtail.clone(); //Initialize these partial forces and moments using
+
+    // Partial moment at the base plate (body B) / yaw bearing (point O) due the nacelle, generator, and rotor [-]
+
+    rt_hs.pmom_bnc_rt = rt_hs.pmom_ngn_rt.clone() + rt_hs.pmom_ntail.clone(); // the rotor, rotor-furl, generator, and tail effects
+
+  
+
+    for i in 0..p.dofs.n_actv_dof as usize{
+
+        tmp_vec = cross_product(&rt_hs.r_ov, &rt_hs.pfrc_vgn_rt.slice(s![.., p.dofs.srt_ps[i] - 1]).to_owned()); // The portion of PMomBNcRt associated with the PFrcVGnRt
+
+        let value = rt_hs.pmom_bnc_rt.slice(s![.., p.dofs.srt_ps[i]-1]).to_owned() + tmp_vec;
+
+        rt_hs.pmom_bnc_rt.slice_mut(s![.., p.dofs.srt_ps[i]-1]).assign(&value);
+
+    }
+
+    for i in 0.. p.dofs.npie as usize{
+
+        tmp_vec = cross_product(&rt_hs.r_ow, &rt_hs.pfrc_wtail.slice(s![.., p.dofs.pie[i] - 1]).to_owned()); // The portion of PMomBNcRt associated with the PFrcWTail
+
+        let value = rt_hs.pmom_bnc_rt.slice(s![.., p.dofs.pie[i]-1]).to_owned() + tmp_vec;
+
+        rt_hs.pmom_bnc_rt.slice_mut(s![.., p.dofs.pie[i]-1]).assign(&value);
+
+    }
+
+    for i in 0.. p.dofs.npue as usize{
+
+        tmp_vec1 = -p.nac_mass * rt_hs.plin_vel_eu.slice(s![p.dofs.pue[i] -1, 0, ..]).to_owned(); //The portion of PFrcONcRt associated with the NacMass
+
+        tmp_vec2 = cross_product(&rt_hs.r_ou, &tmp_vec1); // The portion of PMomBNcRt associated with the NacMass
+
+  
+
+        let value = rt_hs.pfrc_oncrt.slice(s![.., p.dofs.pue[i] -1]).to_owned() + tmp_vec1;
+
+        rt_hs.pfrc_oncrt.slice_mut(s![.., p.dofs.pue[i] -1]).assign(&value);
+
+  
+
+        let value = rt_hs.pmom_bnc_rt.slice(s![.., p.dofs.pue[i] -1]).to_owned() + tmp_vec2 -
+
+                                                                p.nacd2_iner * coord_sys.d2.clone() * dot_product(&coord_sys.d2.clone(), &rt_hs.p_ang_vel_en.slice(s![p.dofs.pue[i] -1, 0, ..]).to_owned());
+
+        rt_hs.pmom_bnc_rt.slice_mut(s![.., p.dofs.pue[i] -1]).assign(&value);
+
+    }
+```

多体+耦合求解器/计算线速度 偏加速度.md

@@ -0,0 +1,42 @@
+
+# yaw
+```rust
+ewn_x_r_ou = cross_product(&rt_hs.ang_vel_en, &rt_hs.r_ou);
+
+
+rt_hs.plin_vel_eu = rt_hs.plin_vel_eo.clone();
+
+for i in 0..NPN{
+
+	tmp_vec0 = cross_product(&rt_hs.p_ang_vel_en.slice(s![PN[i] - 1, 0, ..]).to_owned(), &rt_hs.r_ou);
+
+	tmp_vec1 = cross_product(&rt_hs.p_ang_vel_en.slice(s![PN[i] - 1, 0, ..]).to_owned(), &ewn_x_r_ou);
+
+	tmp_vec2 = cross_product(&rt_hs.p_ang_vel_en.slice(s![PN[i] - 1, 1, ..]).to_owned(), &rt_hs.r_ou);
+
+
+
+	let update_value = tmp_vec0 + rt_hs.plin_vel_eu.slice(s![PN[i] - 1, 0, ..]);
+
+	// Partial linear velocity (and its 1st time derivative) of the nacelle center of mass (point U) in the inertia frame (body E for earth) [-]
+
+	rt_hs.plin_vel_eu.slice_mut(s![PN[i] - 1, 0, ..]).assign(&update_value);
+
+
+
+	let update_value = tmp_vec1 + tmp_vec2 + rt_hs.plin_vel_eu.slice(s![PN[i] - 1, 1, ..]);
+
+	rt_hs.plin_vel_eu.slice_mut(s![PN[i] - 1, 1, ..]).assign(&update_value);
+
+	// Linear acceleration of the nacelle center of mass (point U) in the inertia frame (body E for earth) (excluding QD2T components) [-]
+
+	rt_hs.lin_acc_eut = rt_hs.lin_acc_eut.clone() + x.qdt[PN[i] as usize - 1] * rt_hs.plin_vel_eu.slice(s![PN[i] - 1, 1, ..]).to_owned();
+
+    }
+```
+
+plin_vel_eu 
+Partial linear velocity (and its 1st time derivative) of the nacelle center of mass (point U) in the inertia frame (body E for earth) [-]
+
+lin_acc_eut
+Linear acceleration of the nacelle center of mass (point U) in the inertia frame (body E for earth) (excluding QD2T components) [-]

多体+耦合求解器/计算角度 大小 速度 偏加速度.md

@@ -0,0 +1,24 @@
+
+
+# yaw
+
+```rust
+// Partial angular velocity of the nacelle (body N) in the inertia frame (body E for earth) [-]
+
+
+rt_hs.p_ang_vel_en.slice_mut(s![.., 0, ..]).assign(&rt_hs.p_ang_vel_eb.slice_mut(s![.., 0, ..]));
+
+rt_hs.p_ang_vel_en.slice_mut(s![DOF_YAW -1, 0, ..]).assign(&coord_sys.d2.clone());
+
+rt_hs.ang_vel_en = rt_hs.ang_vel_eb.clone() + x.qdt[DOF_YAW as usize- 1] * rt_hs.p_ang_vel_en.slice_mut(s![DOF_YAW -1, 0, ..]).to_owned();
+
+
+rt_hs.p_ang_vel_en.slice_mut(s![.., 1, ..]).assign(&rt_hs.p_ang_vel_eb.slice_mut(s![.., 1, ..]));
+
+let p_ang_vel_en_slice = rt_hs.p_ang_vel_en.slice(s![DOF_YAW - 1, 0, ..]).to_owned();
+
+rt_hs.p_ang_vel_en.slice_mut(s![DOF_YAW - 1, 1, ..]).assign(&cross_product(&rt_hs.ang_vel_eb, &p_ang_vel_en_slice));
+
+rt_hs.ang_acc_ent = rt_hs.ang_acc_ebt.clone() + x.qdt[DOF_YAW as usize- 1] * rt_hs.p_ang_vel_en.slice_mut(s![DOF_YAW - 1, 1, ..]).to_owned();
+```
+

多体求解器debug/多体+气动 yaw debug.md

@@ -0,0 +1,36 @@
+
+# 问题
+转速在14s之后一直掉
+![[Pasted image 20250120102349.png]]
+
+## yaw求解过程
+
+
+1 输入yaw_mom from 控制
+
+
+multibody_solution 1834-1846行
+
+Elastodyn.f90 8295
+FAST_Subs.f90
+- 4835
+- 4520
+- 4865
+
+pmom_bnc_rt  在基板 (point O) 处由机舱、发电机和转子产生的偏力矩 [-] 2方向
+Partial moment at the base plate (body B) / yaw bearing (point O) due the nacelle, generator, and rotor [-]
+- 2, 10: yaw 差距较小    3-11
+- 2, 12: geaz  差距较大  3-13
+- 2, 13: drtr 差距较大     3-14
+
+
+pmom_ngn_rt 就有问题
+Partial moment at the nacelle (body N) / selected point on rotor-furl axis (point V) due the structure that furls with the rotor, generator, and rotor [-]
+
+pmom_lprot 有问题 （2，10）
+
+
+
+pfrc_prot 有问题
+plin_vel_ec 10, 0, 0有问题
+Partial linear velocity (and its 1st time derivative) of the hub center of mass (point C) in the inertia frame (body E for earth) [-]

多体求解器debug/多体+气动 转速 debug.md

@@ -1,4 +0,0 @@
-
-# 问题
-转速在30s之后一直掉
-![[Pasted image 20250110111923.png]]

杂项/b450 mortar主板.md

@@ -0,0 +1,9 @@
+
+PCI_E1 PCIe 3.0 x16 
+PCI_E2 PCIe 2.0 x1 
+PCI_E3 PCIe 2.0 x1 
+PCI_E4 PCIe 2.0 x4 
+
+当在 M2_2 接口中安装了 M.2 固态硬盘时，PCI_E4 插槽将无效。  
+
+当在 PCI_E3 插槽中安装扩展卡时，PCI_E2 插槽将无效。