17 lines
3.1 KiB
Plaintext
17 lines
3.1 KiB
Plaintext
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{"id":"330ceae2327436f1","type":"text","text":"牛顿-欧拉方程\n\n$$\n\\begin{split}\\bar{F} = & \\frac{{}^N d \\bar{p}}{dt} \\quad \\textrm{ where } \\bar{p} = m_B{}^N\\bar{v}^{B_o} \\\\\\bar{M} = & \\frac{{}^N d\\bar{H}}{dt} \\quad \\textrm{ where }\\bar{H} = \\breve{I}^{B/B_o} \\cdot {}^N\\bar{\\omega}^{B}\\end{split}|","x":-242,"y":-194,"width":542,"height":174},
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{"id":"04fa17192ff0596c","type":"text","text":"GAF Generalized Active Force 左端项","x":-448,"y":160,"width":250,"height":60},
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{"id":"3dd1bf823248bf74","type":"text","text":"完整约束(holonomic)\n**约束方程中不包含坐标对时间的导数(不包含运动约束)**，或者约束方程中的微分项可以积分为有限形式的约束（几何约束或可积分的运动约束）\n$f_s(x_k, y_k, z_k;;t)=0$\n$f_s(x_k, y_k, z_k;\\dot{x_k},\\dot{y_k},\\dot{z_k};t)=0$","x":960,"y":-214,"width":340,"height":214},
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{"id":"3f3febc750ff1af8","type":"text","text":"非完整约束(nonholonomic)\n**约束方程中包含坐标对时间的导数（包含运动约束，对广义速度u1...ur的约束）**，且不可能积分成有限形式的约束（包括积分的运动约束）\n$f_s(x_k, y_k, z_k;\\dot{x_k},\\dot{y_k},\\dot{z_k};t)=0$","x":960,"y":60,"width":340,"height":200},
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{"id":"c574d94bf9b233b4","type":"text","text":"GIF Generalized Inertia Force 右端项","x":231,"y":160,"width":250,"height":60},
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{"id":"027a3e957d393870","type":"text","text":"对于holonomic系统中的刚体B，质量$m_B$，质量中心$B_o$，中心inertia dyadic $\\breve{I}^{B/Bo}$。\n$(F_r^*)_B := {}^A\\bar{v}^{B_o}_r \\cdot \\bar{R}^* + {}^A\\bar{\\omega}^B_r \\cdot \\bar{T}^*$\n${}^A\\bar{v}^{B_o}_r$对广义速度$u_r$的偏速度\n${}^A\\bar{\\omega}^B_r$对广义速度$u_r$的偏角速度\n inertia force on the body:\n $\\bar{R}^* := -m_{B} {}^A\\bar{a}^{B_o}$\n ${}^A\\bar{a}^{B_o}$ $B_0$在A的线加速度\n _inertia torque_ on the body:\n $\\bar{T}^* := -\\left({}^A\\bar{\\alpha}^B \\cdot \\breve{I}^{B/Bo} +{}^A\\bar{\\omega}^B \\times\\breve{I}^{B/Bo} \\cdot {}^A\\bar{\\omega}^B\\right)$\n${}^A\\bar{\\alpha}^B$ $B$在A的角加速度\n \n ","x":126,"y":300,"width":460,"height":320},
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{"id":"4fb6c3b08416426b","x":-537,"y":300,"width":429,"height":220,"type":"text","text":"对于holonomic系统中的刚体B，B上的力表示为一个作用与B上Q点的合力与合力偶。\n$(F_r)_B := {}^A\\bar{v}^Q_r \\cdot \\bar{R} + {}^A\\bar{\\omega}^B_r \\cdot \\bar{T}$\n${}^A\\bar{v}^Q_r$对广义速度$u_r$的偏速度\n${}^A\\bar{\\omega}^B_r$对广义速度$u_r$的偏角速度\n$\\bar{R}$ 作用线通过B上Q点的合力，Q可以是质量中心$B_o$\n$\\bar{T}$ B上的扭矩"}
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