From c9b78dfa805a12cb82cb23fc1b7a5570181032ef Mon Sep 17 00:00:00 2001 From: yz Date: Thu, 16 Jan 2025 15:27:27 +0800 Subject: [PATCH] 1 --- .obsidian/plugins/copilot/data.json | 48 ++++++------------- .../auto/Kane-Dynamics-Theory-Applications.md | 25 +++++----- 多体+耦合求解器/思路.canvas | 11 +++++ 多体+耦合求解器/理论框架.canvas | 4 +- 4 files changed, 41 insertions(+), 47 deletions(-) create mode 100644 多体+耦合求解器/思路.canvas diff --git a/.obsidian/plugins/copilot/data.json b/.obsidian/plugins/copilot/data.json index f82cd90..565c251 100644 --- a/.obsidian/plugins/copilot/data.json +++ b/.obsidian/plugins/copilot/data.json @@ -13,16 +13,12 @@ "googleApiKey": "", "openRouterAiApiKey": "", "defaultChainType": "llm_chain", -<<<<<<< HEAD - "defaultModelKey": "gemma2:latest|ollama", -======= "defaultModelKey": "phi4:latest|ollama", ->>>>>>> 43e7b08163ff98d031f47a55e6d8abfb871edb14 "embeddingModelKey": "nomic-embed-text|ollama", "temperature": 0.1, "maxTokens": 1000, "contextTurns": 15, - "userSystemPrompt": "翻译成中文", + "userSystemPrompt": "", "openAIProxyBaseUrl": "", "openAIEmbeddingProxyBaseUrl": "", "stream": true, @@ -47,47 +43,21 @@ "provider": "openai", "enabled": true, "isBuiltIn": true, - "core": true, - "baseUrl": "", - "apiKey": "" + "core": true }, { "name": "gpt-4o-mini", "provider": "openai", "enabled": true, "isBuiltIn": true, - "core": true, - "baseUrl": "", - "apiKey": "" + "core": true }, { "name": "claude-3-5-sonnet-latest", "provider": "anthropic", "enabled": true, "isBuiltIn": true, - "core": true, - "baseUrl": "", - "apiKey": "" - }, - { - "name": "llama3.2:latest", - "provider": "ollama", - "baseUrl": "https://possibly-engaged-filly.ngrok-free.app", - "apiKey": "", - "enabled": true, - "isBuiltIn": false, - "enableCors": true, - "isEmbeddingModel": false - }, - { - "name": "gemma2:latest", - "provider": "ollama", - "baseUrl": "https://possibly-engaged-filly.ngrok-free.app", - "apiKey": "", - "enabled": true, - "isBuiltIn": false, - "enableCors": true, - "isEmbeddingModel": false + "core": true }, { "name": "phi4:latest", @@ -98,6 +68,16 @@ "isBuiltIn": false, "enableCors": true, "isEmbeddingModel": false + }, + { + "name": "llama3.2:latest", + "provider": "ollama", + "baseUrl": "https://possibly-engaged-filly.ngrok-free.app", + "apiKey": "", + "enabled": true, + "isBuiltIn": false, + "enableCors": true, + "isEmbeddingModel": false } ], "activeEmbeddingModels": [ diff --git a/力学书籍/Kane-Dynamics-Theory-Applications/auto/Kane-Dynamics-Theory-Applications.md b/力学书籍/Kane-Dynamics-Theory-Applications/auto/Kane-Dynamics-Theory-Applications.md index 404348d..7a74bb9 100644 --- a/力学书籍/Kane-Dynamics-Theory-Applications/auto/Kane-Dynamics-Theory-Applications.md +++ b/力学书籍/Kane-Dynamics-Theory-Applications/auto/Kane-Dynamics-Theory-Applications.md @@ -3617,31 +3617,34 @@ and the ellipsoid appears as shown in Fig. 3.9.2. Furthermore, the moment of ine # GENERALIZED FORCES -The necessity to cross-multiply a vector $\mathbf{v}$ with the position vector ${\mathfrak{p}}^{A B}$ from a point $A$ to a point $B$ arises frequently [see, for example, Eqs. (2.7.1) and (3.5.27)]. Now, ${\bf p}^{A B}\mathrm{\bf~\times~}{\bf v}={\bf p}^{A C}\mathrm{\bf~\times~}{\bf v},$ where $\mathfrak{p}^{A C}$ is the position vector from $A$ to any point C of the line L that is parallel to v and passes through B; and, when C is chosen properly, it may be easier to evaluate $\mathsf{\pmb{p}}^{A C}$ x v than $\boldsymbol{\mathsf{p}}^{A B}\,\times\,\boldsymbol{\mathsf{v}}.$ This fact provides the motivation for introducing the concepts of “bound" vectors and “moments" of such vectors as in Sec. 4.1. The terms “couple” and “torque,” which have to do with special sets of bound vectors, are defined in Sec. 4.2, and the concepts of "equivalence" and “replacement,” each of which involves two sets of bound vectors, are discussed in Sec. 4.3. This material then is used throughout the rest of the chapter to facilitate the forming of expressions for quantities that play a preeminent role in connection with dynamical equations of motion, namely, two kinds of generalized forces. Sections 4.4-4.10 deal with generalized active forces, which come into play whenever the particles of a system are subject to the actions of contact and/or distance forces. Generalized inertia forces, which depend on both the motion and the mass distribution of a system, are discussed in Sec. 4.11. Mastery of the material brings one into position to formulate dynamical equations for any system possessing a finite number of degrees of fredom, as may be ascertained by reading Sec. 6.1. +The necessity to cross-multiply a vector $\mathbf{v}$ with the position vector ${\mathfrak{p}}^{A B}$ from a point $A$ to a point $B$ arises frequently [see, for example, Eqs. (2.7.1) and (3.5.27)]. Now, ${\bf p}^{A B}\mathrm{\bf~\times~}{\bf v}={\bf p}^{A C}\mathrm{\bf~\times~}{\bf v},$ where $\mathfrak{p}^{A C}$ is the position vector from $A$ to any point C of the line L that is parallel to v and passes through B; and, when C is chosen properly, it may be easier to evaluate $\mathsf{\pmb{p}}^{A C}$ x v than $\boldsymbol{\mathsf{p}}^{A B}\,\times\,\boldsymbol{\mathsf{v}}.$ This fact provides the motivation for introducing the concepts of “bound" vectors and “moments" of such vectors as in Sec. 4.1. The terms “couple” and “torque,” which have to do with special sets of bound vectors, are defined in Sec. 4.2, and the concepts of "equivalence" and “replacement,” each of which involves two sets of bound vectors, are discussed in Sec. 4.3. This material then is used throughout the rest of the chapter to facilitate the forming of expressions for quantities that play a preeminent role in connection with dynamical equations of motion, namely, two kinds of generalized forces. Sections 4.4-4.10 deal with generalized active forces, which come into play whenever the particles of a system are subject to the actions of contact and/or distance forces. Generalized inertia forces, which depend on both the motion and the mass distribution of a system, are discussed in Sec. 4.11. Mastery of the material brings one into position to formulate dynamical equations for any system possessing a finite number of degrees of freedom, as may be ascertained by reading Sec. 6.1. # 4.1 MOMENT ABOUT A POINT, BOUND VECTORS, RESULTANT Of the infinitely many lines that are parallel to every vector v, a particular one, say，, $L$ , called the line of action of v, must be selected before M, the moment of $\mathbf{v}$ aboutapoint $P$ , can be evaluated, for M is defined as +$$ +M\triangleq{p}\times{v} +$$ -wherepis thepositionvector from $P$ to any point on $L$ Once $L$ hasbeenspecified, $\gamma$ is said to be a bound vector, and it is customary to show $\mathbf{v}$ on $L$ in pictorial representations of $\gamma$ A vector for which no line of action is specified is called a free vector. +where $p$ is the position vector from $P$ to any point on $L$ Once $L$ has been specified, $v$ is said to be a bound vector, and it is customary to show $\mathbf{v}$ on $L$ in pictorial representations of $v$. A vector for which no line of action is specified is called a free vector. -The resultant $\mathbf{R}$ ofa set $\boldsymbol{S}$ of vectors $\mathbf{\nu}_{1},\dots,\mathbf{\nu}_{v}$ is defined as +The resultant $\mathbf{R}$ of a set $\boldsymbol{S}$ of vectors $\mathbf{\nu}_{1},\dots,\mathbf{\nu}_{v}$ is defined as $$ -\mathbb{R}\triangleq\sum_{i=1}^{\nu}\mathbb{v}_{i} +{R}\triangleq\sum_{i=1}^{\nu}{v}_{i} $$ and,if $\mathbf{v}_{1},\ldots,\mathbf{v}_{\nu}$ are bound vectors, the sum of their moments about a point $P$ is called the moment of S about P. -At times, it is convenient to regard the resultant $\mathbf{k}$ of a set ${\cal{S}}$ of boundvectors $\mathbf{\nu}_{1},\dots,\mathbf{v}_{\nu}$ as a bound vector. Suppose, for example, that $\mathbf{M}^{\mathbf{s}/P}$ and ${\bf{M}}^{s/Q}$ denote the moments of ${\cal{S}}$ about points $P$ and $\mathcal{Q}$ respectivly, and $\mathbf{R}$ isregarded as abound vector whose line of action passesthrough $\boldsymbol{Q}$ . Then one can find ${\bf M}^{{\bf S}/{P}}$ simply by adding to $\mathbf{M}^{S/Q}$ themoment of Rabout $P$ for +At times, it is convenient to regard the resultant $R$ of a set ${\cal{S}}$ of boundvectors $\mathbf{\nu}_{1},\dots,\mathbf{v}_{\nu}$ as a bound vector. Suppose, for example, that $\mathbf{M}^{\mathbf{S}/P}$ and ${\bf{M}}^{S/Q}$ denote the moments of ${\cal{S}}$ about points $P$ and $\mathcal{Q}$ respectivly, and $\mathbf{R}$ isregarded as abound vector whose line of action passesthrough $\boldsymbol{Q}$ . Then one can find ${\bf M}^{{\bf S}/{P}}$ simply by adding to $\mathbf{M}^{S/Q}$ themoment of Rabout $P$ for $$ \mathbf{M}^{S/P}=\mathbf{M}^{S/Q}+\mathbf{r}^{P Q}\times\mathbf{R} $$ -Where $\mathbf{r}^{P Q}$ is the positionvector from $P$ to $\mathcal{Q}$ +Where $\mathbf{r}^{P Q}$ is the position vector from $P$ to $\mathcal{Q}$ -DerivationLet and be the position vectors from $P$ and $\mathcal{Q}$ respetivly,to a $\mathbf{p}_{i}$ ${\bf q}_{i}$ +Derivation Let and be the position vectors from $P$ and $\mathcal{Q}$ respetivly,to a $\mathbf{p}_{i}$ ${\bf q}_{i}$ point on the line of action $L_{i}$ of $\mathbf{v}_{i}\,(i=1,\ldots,\nu)$ ,and let be the position vector from $P$ to $\mathcal{Q}$ , as shown in Fig. 4.1.1. Then, by defnition, @@ -3726,7 +3729,7 @@ $$ A couple is a set of bound vectors (see Sec. 4.1) whose resultant (see Sec.4.1) is equal to zero.A couple consisting of only two vectors is called a simple couple. Hence, the vectors forming a simple couple necessarily have equal magnitudes andoppositedirections. -Couples are not vectors,for a set of vectors is not a vector, any more than a set of points is a point; but there exists a unique vector, called the torque of the couple,that is intimately associated with a couple,namely,the moment of the couple about a point. It is unique because, as can be seen by reference to Eq. (4.1.3), a couplehas thesamemomentabout allpoints. +Couples are not vectors, for a set of vectors is not a vector, any more than a set of points is a point; but there exists a unique vector, called the torque of the couple, that is intimately associated with a couple, namely, the moment of the couple about a point. It is unique because, as can be seen by reference to Eq. (4.1.3), a couple has the same moment about all points. Example Four forces, $\mathbf{F}_{1},\ldots,\mathbf{F}_{4}$ , have the lines of action shown in Fig. 4.2.1, and the magnitudes of $\mathbf{F}_{1},\ldots,\mathbf{F}_{4}$ are proportional to the lengths of the lines $A B$ ,BC, $C D$ ,and $D A$ ,respectively; that is, @@ -3856,7 +3859,7 @@ The method just used to arrive at Eq. (14) has one major faw, which is that it i # 4.4 GENERALIZED ACTIVE FORCES -Ⅱ $\mathbf{\dot{\boldsymbol{u}}}_{1},\ldots,\mathbf{\boldsymbol{u}}_{n}$ are generalized speeds for a simple nonholonomic system $s$ possessing $p$ degrees o freedom in a reference frame $A$ (see Sec.2.13), $p$ quantities $\boldsymbol{\tilde{F}}_{1},...,\boldsymbol{\tilde{F}}_{p}$ callednonholonomicgeneralizedactiveforcesfor $s$ .n $A$ and $n$ quantities $F_{1},\ldots,F_{n}$ called holonomic generalized active forces for $s$ in $A$ , are defined as +If $\mathbf{{\boldsymbol{u}}}_{1},\ldots,\mathbf{\boldsymbol{u}}_{n}$ are generalized speeds for a simple nonholonomic system $s$ possessing $p$ degrees of freedom in a reference frame $A$ (see Sec.2.13), $p$ quantities $\boldsymbol{\tilde{F}}_{1},...,\boldsymbol{\tilde{F}}_{p}$ callednonholonomicgeneralizedactiveforcesfor $s$ .n $A$ and $n$ quantities $F_{1},\ldots,F_{n}$ called holonomic generalized active forces for $s$ in $A$ , are defined as $$ \widetilde{F}_{r}\triangleq\sum_{i\,=\,1}^{\nu}\widetilde{\mathbf{v}}_{r}^{\,\,P_{i}}\cdot{\mathbf{R}}_{i}\qquad(r=1,\ldots,p) @@ -3878,7 +3881,7 @@ $$ As in the case of holonomic and nonholonomic partial angular velocities and partial velocities, one can generally omit the adjectives “holonomic” and “nonholonomic” when speaking of generalized forces, but the tilde notation should be used to distinguish the two kinds of generalized active forces from each other. -Derivation Referring to Eq. (2.14.17) to express $\tilde{\mathbf{v}}_{r}^{\;\,P_{i}}\;(r=1,\dots,p)$ in termsof $\mathbf{v}_{s}^{\,\,p_{i}}$ $s=p+1,\ldots,n)$ ,onehas +Derivation Referring to Eq. (2.14.17) to express $\tilde{\mathbf{v}}_{r}^{\;\,P_{i}}\;(r=1,\dots,p)$ in terms of $\mathbf{v}_{s}^{\,\,p_{i}}$ $s=p+1,\ldots,n)$ ,one has $$ \begin{array}{l}{{\displaystyle{\widetilde F}_{r}=\sum_{\scriptscriptstyle(1)\;i=1}^{\nu}\left({\bf v}_{r}{}^{P_{i}}+\sum_{\scriptscriptstyle s=p+1}^{n}{\bf v}_{s}{}^{P_{i}}A_{s r}\right)\cdot{\bf R}_{i}}\ ~}\\ {{\displaystyle=\sum_{i=1}^{\nu}{\bf v}_{r}{}^{P_{i}}\cdot{\bf R}_{i}+\sum_{\scriptscriptstyle s=p+1}^{n}\left(\sum_{\scriptscriptstyle i=1}^{\nu}{\bf v}_{s}{}^{P_{i}}\cdot{\bf R}_{i}\right)A_{s r}}\qquad(r=1,\ldots,p)}\end{array} @@ -3886,7 +3889,7 @@ $$ and use of Eqs. (2) then leads immediately to Eqs. (3). -Example In Fig. 4.4.1, $\boldsymbol{P}_{1}$ and $P_{2}$ designate particles of masses $m_{1}$ and $m_{2}$ that can slidefreelyin a smooth tube $T$ and are attached to light linear springs $\sigma_{1}$ and $o_{2}$ having spring constants $k_{1}$ and $k_{2}$ and “natural" lengths $L_{1}$ and $L_{2}$ $T$ ismadetorotate aboutafixedhorizontal axispassingthroughoneend of $T$ in such a way that the anglebetween thevertical and the axis of $T$ is a prescribed function $\theta(t)$ of the time $t$ Generalized active forces $\boldsymbol{F}_{1}$ and $\boldsymbol{F}_{2}$ associatedwithgeneralizedspeeds $\boldsymbol{u}_{1}$ and $u_{2}$ defined as +Example In Fig. 4.4.1, $\boldsymbol{P}_{1}$ and $P_{2}$ designate particles of masses $m_{1}$ and $m_{2}$ that can slide freely in a smooth tube $T$ and are attached to light linear springs $\sigma_{1}$ and $o_{2}$ having spring constants $k_{1}$ and $k_{2}$ and “natural" lengths $L_{1}$ and $L_{2}$ $T$ is made to rotate aboutafixedhorizontal axispassingthroughoneend of $T$ in such a way that the anglebetween thevertical and the axis of $T$ is a prescribed function $\theta(t)$ of the time $t$ Generalized active forces $\boldsymbol{F}_{1}$ and $\boldsymbol{F}_{2}$ associatedwithgeneralizedspeeds $\boldsymbol{u}_{1}$ and $u_{2}$ defined as $$ u_{r}\triangleq\dot{q}_{r}\qquad(r=1,2) diff --git a/多体+耦合求解器/思路.canvas b/多体+耦合求解器/思路.canvas new file mode 100644 index 0000000..d4fee2b --- /dev/null +++ b/多体+耦合求解器/思路.canvas @@ -0,0 +1,11 @@ +{ + "nodes":[ + {"id":"4b7faf7953451d56","x":-140,"y":-160,"width":250,"height":60,"type":"text","text":"1、debug转速"}, + {"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":"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":"e52009c9149e427f","x":160,"y":-160,"width":250,"height":60,"type":"text","text":"模块稳定性"} + ], + "edges":[ + {"id":"2a6d49446576cbc8","fromNode":"4b7faf7953451d56","fromSide":"right","toNode":"e52009c9149e427f","toSide":"left"} + ] +} \ No newline at end of file diff --git a/多体+耦合求解器/理论框架.canvas b/多体+耦合求解器/理论框架.canvas index 34c2e19..19b1e6d 100644 --- a/多体+耦合求解器/理论框架.canvas +++ b/多体+耦合求解器/理论框架.canvas @@ -5,8 +5,8 @@ {"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","x":-280,"y":340,"width":250,"height":60,"type":"text","text":"广义坐标"}, - {"id":"8ec17237cebe7433","x":60,"y":340,"width":250,"height":60,"type":"text","text":"广义速率"} + {"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} ], "edges":[ {"id":"647c1b45edc92b02","fromNode":"9461f7dd96103316","fromSide":"bottom","toNode":"0c8534c8ba68c9a6","toSide":"top"},