From 0e3b09c98a354ef3dba9846c3d595b87c810b428 Mon Sep 17 00:00:00 2001 From: gyz Date: Sun, 27 Apr 2025 14:42:28 +0800 Subject: [PATCH] vault backup: 2025-04-27 14:42:27 --- ...of Multibody Systems (Shabana A.A.) (Z-Library).md | 12 +++++++----- 工作总结/周报/周报74-郭翼泽.docx | Bin 0 -> 20617 bytes 2 files changed, 7 insertions(+), 5 deletions(-) create mode 100644 工作总结/周报/周报74-郭翼泽.docx diff --git a/力学书籍/力学/Dynamics of Multibody Systems (Shabana A.A.) (Z-Library)/auto/Dynamics of Multibody Systems (Shabana A.A.) (Z-Library).md b/力学书籍/力学/Dynamics of Multibody Systems (Shabana A.A.) (Z-Library)/auto/Dynamics of Multibody Systems (Shabana A.A.) (Z-Library).md index d015273..772f2be 100644 --- a/力学书籍/力学/Dynamics of Multibody Systems (Shabana A.A.) (Z-Library)/auto/Dynamics of Multibody Systems (Shabana A.A.) (Z-Library).md +++ b/力学书籍/力学/Dynamics of Multibody Systems (Shabana A.A.) (Z-Library)/auto/Dynamics of Multibody Systems (Shabana A.A.) (Z-Library).md @@ -6833,15 +6833,17 @@ In this equation, $\pmb{\alpha}^{i}$ is the angular acceleration vector. The ter 在这个方程中,$\pmb{\alpha}^{i}$ 是角加速度矢量。$\ddot{\mathbf{R}}^{i}$ 是刚体参考系原点的绝对加速度。第二项,$\boldsymbol{\omega}^{i}\times(\boldsymbol{\omega}^{i}\times\mathbf{u}^{i})$ ,是与点 $P^{\prime}$ 瞬时重合且不发生变形的 $P$ 点的加速度的法向分量。该加速度分量沿连接两个点 $o$ 和 $P$ 的直线方向。第三项,$\propto^{i}\times\mathbf{u}^{i}$ ,是相对于 $o$ 点的 $P^{i}$ 点的切向加速度分量。该分量的方向垂直于角加速度矢量 $\alpha^{i}$ 和矢量 $\mathbf{u}^{i}$。第四项,$2\omega^{i}\times(\mathbf{A}^{i}\dot{\mathbf{u}}^{i})$ ,是科里奥利加速度分量,第五项,$\mathbf{A}^{i}\ddot{\mathbf{u}}^{i}$ 是由于变形相对于刚体参考系的 $P$ 点的加速度。如果刚体是刚性的,则第四项和第五项消失。 Example 5.2 The reference of the beam of Example 1 rotates with a constant angular velocity $\omega={\dot{\theta}}=5$ rad/sec. Determine the absolute velocity and acceleration of the tip point $A$ at the instant of time $t$ at which the beam coordinates, velocities, and accelerations are given by - +示例 5.2 +示例 1 中的梁以常数角速度 $\omega={\dot{\theta}}=5$ rad/sec 旋转。确定在梁坐标、速度和加速度给定时,时间 $t$ 瞬时尖端点 $A$ 的绝对速度和绝对加速度。 $$ \begin{array}{r l}{\mathbf{q}=\left[\mathbf{q}_{r}^{\mathrm{T}}\quad\mathbf{q}_{f}^{\mathrm{T}}\right]^{\mathrm{T}}=\left[R_{1}\quad R_{2}\quad\theta\quad q_{f1}\quad q_{f2}\right]^{\mathrm{T}}}&{}\\ {=\left[1.0\quad0.5\quad30^{\circ}\quad0.001\quad0.01\right]^{\mathrm{T}}}&{}\\ {\dot{\mathbf{q}}=\left[\dot{\mathbf{q}}_{r}^{\mathrm{T}}\quad\dot{\mathbf{q}}_{f}^{\mathrm{T}}\right]^{\mathrm{T}}=\left[\dot{R}_{1}\quad\dot{R}_{2}\quad\dot{\theta}\quad\dot{q}_{f1}\quad\dot{q}_{f2}\right]^{\mathrm{T}}}&{}\\ {=\left[0.1\quad1.0\quad5\quad2\quad3\right]^{\mathrm{T}}}&{}\\ {\ddot{\mathbf{q}}=\left[\ddot{\mathbf{q}}_{r}^{\mathrm{T}}\quad\ddot{\mathbf{q}}_{f}^{\mathrm{T}}\right]^{\mathrm{T}}=\left[\ddot{R}_{1}\quad\ddot{R}_{2}\quad\ddot{\theta}\quad\ddot{q}_{f1}\quad\ddot{q}_{f2}\right]^{\mathrm{T}}}&{}\\ {=\left[2\quad0\quad0\quad10\quad20\right]^{\mathrm{T}}}&{}\end{array} $$ Solution In this case the matrix $\mathbf{L}$ of Eq. 22 is the $2\times5$ matrix +解决方案 在本例中,公式22中的矩阵 $\mathbf{L}$ 是一个 $2\times5$ 矩阵。 $$ -{\bf L}=[{\bf I}\cdot\mathrm{~\bf~B~}\;\mathrm{~\bf~AS}] +{\bf L}=[{\bf ~I~}~\mathrm{~\bf~B~}\;\mathrm{~\bf~AS}] $$ where $\mathbf{I}$ is the $2\times2$ identity matrix @@ -6865,7 +6867,7 @@ $$ From Example 1, the vector $\bar{\mathbf{u}}_{A}$ , which is the position of the tip point $A$ defined in the beam coordinate system, is given by $\bar{\mathbf{u}}_{A}=[0.501\quad0.01]^{\mathrm{T}}$ . Therefore, the vector $\mathbf{B}$ can be evaluated as $$ -\mathbf{B}=\mathbf{A}_{\theta}\bar{\mathbf{u}}_{A}=\left[{\bf\Pi}_{0.866}^{-0.5}\quad{-0.866}\right]\left[{\bf\Pi}_{0.01}^{0.501}\right]=\left[{\bf\Pi}_{0.42886}^{-0.25916}\right] +\mathbf{B}=\mathbf{A}_{\theta}\bar{\mathbf{u}}_{A}={\left[\begin{array}{l l}{-0.5}&{-0.866}\\ {0.866}&{-0.5}\end{array}\right]}{\left[\begin{array}{l}{0.501}\\ {0.01}\end{array}\right]}={\left[\begin{array}{l}{−0.25916}\\ {0.42886}\end{array}\right]} $$ Since at point $A$ , $\xi=(x/l)=1$ , the shape matrix S evaluated at point $A$ is given by @@ -6883,7 +6885,7 @@ $$ The matrix $\mathbf{L}$ can then be defined as $$ -{\bf L}=[{\bf I}{\mathrm{~\boldmath~{~\cal~B~}~}}{\mathrm{~\boldmath~{~\cal~AS}}}]=\left[{\begin{array}{c c c c c}{1}&{0}&{-0.25916}&{0.8660}&{-0.5000}\\ {0}&{1}&{0.42886}&{0.5000}&{0.8660}\end{array}}\right] +{\bf L}=[{\bf ~I~}~\mathrm{~\bf~B~}\;\mathrm{~\bf~AS}]=\left[{\begin{array}{c c c c c}{1}&{0}&{-0.25916}&{0.8660}&{-0.5000}\\ {0}&{1}&{0.42886}&{0.5000}&{0.8660}\end{array}}\right] $$ and accordingly, the global velocity vector of point $A$ is given by @@ -6902,7 +6904,7 @@ where $$ {\begin{array}{r l}{\mathbf{L}{\ddot{\mathbf{q}}}={\left[\begin{array}{l l l l l}{1}&{0}&{-0.25916}&{0.8660}&{-0.5000}\\ {0}&{1}&{0.42886}&{0.500}&{0.8660}\end{array}\right]}{\left[\begin{array}{l}{2}\\ {0}\\ {0}\\ {10}\\ {20}\end{array}\right]}}\\ {={\left[\begin{array}{l}{0.66}\\ {22.32}\end{array}\right]}{\mathrm{m}}/{\mathrm{sec}}^{2}}\end{array}} -$$ +$$ One can verify that the matrix $\dot{\mathbf{L}}$ is $$ \dot{\mathbf{L}}=[\mathbf{0}_{2}\quad\dot{\mathbf{B}}\quad\dot{\mathbf{A}}\mathbf{S}]=[\mathbf{0}_{2}\quad(-\mathbf{A}\bar{\mathbf{u}}_{A}\dot{\theta}+\mathbf{A}_{\theta}\mathbf{S}\dot{\mathbf{q}}_{f})\quad\mathbf{A}_{\theta}\mathbf{S}\dot{\theta}] diff --git a/工作总结/周报/周报74-郭翼泽.docx b/工作总结/周报/周报74-郭翼泽.docx new file mode 100644 index 0000000000000000000000000000000000000000..53e8c0f41b8c4d2f0c43550779213dbb28688832 GIT binary patch literal 20617 zcmeFZgLiFR(k~p_wr$%wv2EM7ZQIU?ZQCcdZR_MD`SNss-M9O8-@o8}*BGnDo~T{5 z=lIQCRdZD>c`0BJ6aX*)2mk;8LI6lha#&A50Dx*R003kF2p}zCJ6mTHTW39G4|@|Q z9XfX#Yl1=$Ac}kdpzrzrd;Jeyfu@v6*+B*b(HHSQ!iThyn+*aGtXF}fNK^`Zea+<6 zqJQFfeLi@T$YKzvU<;?o5}BQDcyq;*=8UZ-jA02a&79b#z-R!ebLL$W8spZaJZBTb z2dEUdpgA`Ljg#)4mdslo5Rer&(i=$&{dRdKNHGwZPx=*0?E4{#jnwVw56jd6dU0W{ z+nmw*4I@*)vEy>{5h{_APH4MpB!H3=NaI|LQc{@rd@4!=em*p-@GH)f5fUHukkd8C zu`l+$&ISLx_Yx@bDw+eSCdi2NuN{y_-)YNlb96Kj&&X-v95{;$sYdAxv;|B&c~I8y?Ddk145ZC zd{GxyJE!R;Z{8F3tL@pq zPxU;R?vgN{kN1o%p=!1VU%65vfGctOg+J>K{TppxU%&wJ|F&iE60lltzDH!gcO>-p zmeq4Kv38=T`-}eXR{bBmKmX;YS0(ma4l=+9+ys3D&2=lR_hS^v(i{ESz*qx^(2|fw z-dMF<`TXEnT?NuPGx#w%zmW9H(%GezASI-$gwcK3 zejg_5_}TPhf>?rbA}C4&HF6dUEa5dgeYy|%h)U%7s0`YIh;nw(h@`P7*Fk0FCEb@f zKZ9{;*-~7~3;ZXqXiq3^#|)+~lqr9G8Z&Kt+`x8&&XDqXQX5l@CFK(hmNf%CX?B8P z6%^KO*W9^hQE%CBLkcD9b-!?)r3&;4;v z)?V!SZO$NA0RRxc7sbua(U{)Y&d9~)+phg(&@Q#K;ugeEd}|lK5Z-d0wj79%l80nN z7AGT1`1O}_N$6Te@1@x~ebx&jRY9BmH8rW4{p0niQ&OlFp`cLtLuFjw7khtU>LsSr z^h465Sw9oD%uabb&15(|M86zX$js7O_aShP)!Oez_Mzt65pLXVpk6ODP9t-v^?|&y z*(bnLZ=wxtR-C`z4wQ?k(j4BE zFFDeTy~vwCBoaW)=^zk68%m#80r&yy(*-oLJrt}Fp3e2d$nRCdK|pTe7=$wim3v35 zkOvfV`j-bMazK*K!j#-aS3(k)&=E{5fh2O_&l3($KuSH6wek3J;~WR{fFC~JuxIr!tyIZhjQH5 zC@wjM7`UA-%lfK>AX_P={-D!>Z@0kIndL0BjaU~9aUahmxz$NK_8&eKh*;Yx1eH8dJ=e<1XpjCNlcOtAiPI$k@)1`|it6%u#IC z0G2a!)(PooBNPV6Zy*b%{%=3avxe9J>$PgtP_!8rJI%23WB zhAvVhTyFZ=yvP_?k?b~$MU)bQ_nFC5tj8h^L{#r>Yw45T&z{j2Q1USYO;gb{0N>qe zA8)qSdfz@i?fhgGM3fe#-)!cGsscY>UQeREr#dyH*tR7dixd`Mc(Lt7=UA{qIiPA3 z07`Dge}}W6X*LS7Lsd(hm=9zKUs$bN4S>$5?NaQs+%S~mFGkjGA;!wCr&!EWiPo16 zxeN%2PeKij;a9AH5)LtJ`fE4aXDiEZ`FU6S?Rml_C@E$GO3Nrb9cPUL)C!!l0tIxd zyps4EG_eA04unChzN*uH^z-+Ab@~`JAQjs2l$(S~yEmZ9@0f@6X%Q1hSH6cVOMZ3c zfwj8AUF-6?JKEjMUGa1<`n+?PoBF+s_J81)wvVYdH)0U+Z}H_7xhqeVRzN!DOrpez zX7p5{%UED=mZ8V3rJCHeAv_b)UR0Ryy0nc^T4>18PRzr9a`@T5xPJYf*D?^f(xG`q_83_IvG4e;%CM>&%!dOAHXhmic<+NFVN_1;Pv1#wYcS5LI-(Yzjl?z zDzhXNMSO*0R~A(oXzBN&__dz4Ai~GefIHZ_Ai6ks3(6X{8)fvs`C>0sNKi>7HE%So zhls7IL;q8lTOZ3Zd1zh47@ zFOdt8-bXxUS$*WEVqD9dHo?yA+t;dmIMtABWQ zfZsvb_w4`KS5@-#UqMLljd+*vA-98KK7n!>dhjB3Ft~lHAjYDRT4`3smX|WE6muj>{^*3&$Pc`3wkITlDM#7T9?GusbzrBeRiLkI;>H7_@Nh&gXDOO1|K* zc!*}P36laem8nE{L)0d4EL0jTj;Wqk7Gs|4ccAFX4{-)5zHk?Dh(0J*TCH>x`~jcU z&ipg@L7F#$Yat%+Q7tpTb$ z75V^&ga6AXb~a$6lX<)f8I8%r*{qX2*2W-GJ$e3M=JVrX!_Y`eQ4p&?TA{0vUVYu| zy;jdQiosM`p|q}vC1|2<*W8R;@(uwY0!cc*i;xmYxAZ05i`!9T>6O#nY11S(_}cQ6M=BY<`lMsOP@e!JiVPGNGq8~{TF zIG!K6SOr$R(xaF<3;H;ri_n5Mt_dfR?Lj=~KqM4A+d=wiIvo-y<&!$rU*InFAq32+ ze13&RYDttiC%?Zhxo29wxLXrQLo5l>N*6K_2!mcdZKH8<(Qy{-Bw~H< zfpnncVlAnaNjs}+`8z3mOM~Wu1z@O9 zPEVrGPQK%Eso35ce*^xXj=zbm@&5zw z5di{;g(OSM#ou^${WrYxH72SEG;3p=q(40DjPi|IU(b>>%Bqhg&sAT|;BE|{)Kip< zR)4&&99Y}@1Mkh>cz@}v)ngM4w-Ct~n4gEB8VoF|&Y>6<1|X4S2ym2DBuO`}&m{gg zxHpXc1$W*Z;Qt@)gZ~%YabY3*aMfP~w?X1{3r?ODqUOp;8Gd>a_#uf`o+kua6k|te z$r5|`%v)kv%#l}@C3ucTJi>Dvq@VZyE8H{w1@0z60hB&j`Ql#9APwPS$g2Kz5N1*3 z1$EUq&{)f#jmtaY@YG+w=R9|#kCLr<9Q>lO8J$3$_4DYK%f~%i1eA; 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