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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},
{"id":"04fa17192ff0596c","type":"text","text":"GAF Generalized Active Force 左端项","x":-448,"y":160,"width":250,"height":60},
{"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},
{"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},
{"id":"4fb6c3b08416426b","type":"text","text":"对于holonomic系统中的刚体BB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","x":-537,"y":300,"width":429,"height":220},
{"id":"c574d94bf9b233b4","type":"text","text":"GIF Generalized Inertia Force 右端项","x":260,"y":160,"width":250,"height":60},
{"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":155,"y":300,"width":460,"height":320},
{"id":"a300bc21279fb24f","type":"text","text":"角加速度 求法","x":155,"y":700,"width":250,"height":60},
{"id":"67a07cb33040e073","type":"text","text":"线加速度 求法","x":510,"y":700,"width":250,"height":60},
{"id":"eeb7df4b945bff86","type":"text","text":"各个部件inertia dyadic求法","x":155,"y":820,"width":250,"height":60},
{"id":"931f7a20403882f5","type":"text","text":"塔架、叶片的GAF GIF求法","x":155,"y":940,"width":250,"height":60},
{"id":"9ba9cf03738bfda2","type":"text","text":"Sympy优势\n- linear acc、angular acc内置方法\n- GIF求解按照公式清晰明了\n\n劣势\n- 不支持柔性体\n- 主动力没有好办法","x":155,"y":1060,"width":355,"height":240},
{"id":"869b7f96937e4202","type":"text","text":"低速轴、高速轴、发电机、摩擦力等求法","x":510,"y":820,"width":250,"height":60},
{"id":"690b6cebbb1e52ad","x":840,"y":700,"width":250,"height":60,"type":"text","text":"是否正确?"},
{"id":"50d5c2753f1f2ec3","x":840,"y":790,"width":250,"height":90,"type":"text","text":"广义主动力还可以怎么求yaw、低速轴、高速轴"},
{"id":"9fc02c3e78a69a7a","x":510,"y":940,"width":250,"height":60,"type":"text","text":"坐标系定义好之后,原点无所谓,有方向即可"},
{"id":"f13fc730aad4e78c","x":840,"y":940,"width":250,"height":180,"type":"text","text":" 偏速度$\\pmb{v}_{\\nu}^{(\\,r\\,)}$ 或 $\\pmb{\\omega}_{i}^{(\\prime)}$ 是将**标量形式的广义速率**赋予**方向性的矢量系数**。从具体算例可以看出, $\\pmb{v}_{\\nu}^{(r)}$ 或 $\\pmb{\\omega}_{i}^{(r)}$ 实际上就是某些基矢量或基矢量的线性组合。"},
{"id":"01e5d049c040e822","x":840,"y":1180,"width":250,"height":220,"type":"text","text":"所谓偏速度 $\\pmb{v}_{\\nu}^{(\\textrm{r})}\\left(\\,r=1\\,,2\\,,\\cdots,f\\right)$ 实际上是某些特定的基矢量或基矢量的线性组合,因此,广义主动力或广义惯性力就是系统内全部主动力或惯性力沿这些特定基矢量方向的投影。"},
{"id":"8867bfcfd58ae90b","x":1180,"y":940,"width":250,"height":120,"type":"text","text":"对于完整系统,凯恩方法中的广义主动力 ${\\boldsymbol{F}}^{(r)}$ 等同于拉格朗日方程中的广义力 $Q_{r}$ 。 "}
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