多刚体系统动力学的正则方程与辛算法

针对多刚体系统动力学数值计算精度的关键问题，首先采用Ｋａｎｅ方程导出了二阶形式的动力学方程，并研究了其中系数矩阵的恒等关系，进而建立了多刚体系统动力学的哈密顿体系并获得正则方程。在此基础上，分析了多刚体系统动力学数值积分的能量耗散现象，揭示其根源在于，数值算法用前一时刻值代替当前值。理论分析和计算结果表明，采用多刚体系统动力学的正则方程与辛算法的结合，可使多体系统动力学的数值计算性态得以改善，能有效消除“能量耗散”现象，从而使动力学计算的误差累积与违约得以控制，保证了计算精度。

Canonical Equations and Symplectic Algorithm for Multi-Rigid-Body System Dynamics

Counters the key problem of improving numerical accuracy of a multi-rigid-bodysystem dynamics. The second order dynamic equations are first established by using Kane'S equation and an identical relationship of the coefficient matrix is found in order to develop theHamiltonian system. The momentum via quasi--coordinate is derived according to Kane'S definition so as to establish the canonical equations. The error accumulation for the known algorithmsis analyzed and the cause of energy dissipation is analyzed which lies in that the last time numerical value is used to represent the present time value. Both theoretical analysis and calculation examples show that the error accumulation of dynamics can be eliminated by using thecanonical equations and symplectic method so that the computational accuracy of multirigidbody system dynamics can be ensured effectively.