Implementation of Kane's Method for a Spacecraft Composed of Multiple Rigid Bodies
Implementation of Kane's Method for a Spacecraft Composed of Multiple Rigid Bodies
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DOI：
10.2514/6.2013-4649
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发表时间：
2013-08
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影响因子：
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通讯作者：
E. Stoneking
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文献类型：
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作者：
E. Stoneking
推导了一般航天器的运动方程，该航天器由通过树形拓扑中的旋转（球形或万向节）接头连接的刚体组成。深入发展了几个支持概念。基二元组有助于从无基向量方程到分量方程的过渡。关节部分允许将 1-DOF、2-DOF、3-DOF 万向节和球形旋转关节抽象为通用符号。由通过关节连接的“内部”主体和“外部”主体组成的基本构建块可以有效地组织任意树结构。凯恩方程以一种有利于大型方程组的系统组装的形式进行了改写，并揭示了凯恩方程与牛顿和欧拉方程之间的关系，而这种关系在通常的表述中是模糊的。所得动力学方程组维数最小，适合计算机数值求解。讨论了实现，并给出了说明性的模拟结果。
Equations of motion are derived for a general spacecraft composed of rigid bodies connected via rotary (spherical or gimballed) joints in a tree topology. Several supporting concepts are developed in depth. Basis dyads aid in the transition from basis-free vector equations to component-wise equations. Joint partials allow abstraction of 1-DOF, 2-DOF, 3-DOF gimballed and spherical rotational joints to a common notation. The basic building block consisting of an "inner" body and an "outer" body connected by a joint enables efficient organization of arbitrary tree structures. Kane's equation is recast in a form which facilitates systematic assembly of large systems of equations, and exposes a relationship of Kane's equation to Newton and Euler's equations which is obscured by the usual presentation. The resulting system of dynamic equations is of minimum dimension, and is suitable for numerical solution by computer. Implementation is discussed, and illustrative simulation results are presented.