刚体动力学方程的一个辛积分方法  

A Symplectic Algorithm for the Dynamics of a Rigid Body

作　　者：路英杰[1] 任革学[1] 

机构地区：[1]清华大学工程力学系,北京100084

出　　处：《应用数学和力学》2006年第1期47-52,共6页Applied Mathematics and Mechanics

摘　　要：针对四元数和对应广义动量表示的刚体定点动力学方程,利用一种位移格式的微分—代数方程积分方案,实现了非独立广义动量表示的拉格朗日方程的辛积分算法.数值实验显示该算法具有精度高和保持系统守恒量的特点.更为重要的是,广义动量表示的拉格朗日方程较之传统形式的拉格朗日方程在辛积分中表现出独特的优越性.For the dynamics of a rigid body with a fixed point based on quatemion and the cormsponding generalized momenta, a displacement-based symplectic integration scheme for differential-algebraic equations is proposed and applied to the Lagrange＇ s equations based on dependent generalized momenta. Numerical experiments show that the algorithm possesses such characters as high precision and preserving system invariants. More importantly, the generalized momenta based Lagrange＇ s equations show unique advantages over the traditional Lagrange＇s equations in symplectic integrations.

关 键 词：刚体动力学 四元数 广义动量 辛积分 

分 类 号：O313.3[理学—一般力学与力学基础]