Symplectic Conservation Integration of Rigid Body Dynamics With Quaternion Parameters
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摘要: 基于刚体定点转动的四元数表示,运用分析结构力学方法,引入离散系统作用量代替四元数微分方程,并在积分点严格满足四元数模等于1的约束条件,进行时间积分.则按分析结构力学理论,不但达到了积分的保辛且区段内部约束条件也可在变分原理意义下近似满足对重陀螺进行数值仿真,结果满意.Abstract: A numerical method was proposed with the quaternion representation of rigid body dynamics. Based on the analytical structural mechanics, the action of differential system was introduced for the time integration of the approximated discrete system and the constraint that the norm of quaternion kept constant at 1 was satisfied strictly at the grid points of integration. As was interpreted in the theory of analytical structural mechanics, the numerical integration was symplectic conservative and the constraint was satisfied approximately in the sense of variation principle. The numerical results of heavy tops are satisfying in precision and efficiency.
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