基于李群离散变分积分子3D摆姿态动力学研究

Attitude dynamics of the 3D pendulum based on the Lie group variational integrator

主要研究了作为地球静止轨道卫星简化模型的3D刚体摆的离散变分积分子求解方法。基于常微分方程的连续求解方法无法保持总能量的计算值在长时间仿真中守恒,导致计算的失真;而离散方法不存在误差积累的问题,故系统的能量能在长时间仿真中守恒,从而保证系统动力学参数的计算值在长时间的仿真中保持稳定。基于李群的离散变分积分子不需要添加约束条件便可保证系统几何结构的守恒,且有较高的计算效率。仿真结果表明:在李群离散变分积分子算法下,处于地球静止轨道上的3D刚体摆的能量,动量及几何结构的计算值都可保持恒定。

The solving method of 3D pendulum variational intergrator is studied as the simplified model of the Geo-stationary spacecraft.The continuous solving method based on the ordinary differential equation can not conserve the total energy as the simulation time increases.There is no error accumulation is discrete method and the energy can be conserved in the long time simulation.The discrete variational integrator based on the Lie group can conserve the geometry character without constraint condition,at a high calculating speed.The simulation result indicates that the Lie group discrete variational integrator can conserve the energy momentum and geometry structure simultaneously.