A Symplectic Algorithm for the Dynamics of a Rigid Body
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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.Abstract: For the dynamics of a rigid body with a fixed point based on quaternion and the corresponding 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.
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Key words:
- rigid_body dynamics /
- quaternion /
- generalized momenta /
- symplectic integration
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