论文部分内容阅读
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。
This paper mainly studies discrete integral solution of 3D rigid body pendulum as a simplified model of geostationary satellites. The continuous solution method based on ordinary differential equation can not keep the calculated value of total energy conserved in long time simulation, which leads to the calculation of distortion. However, the discrete method does not have the problem of error accumulation, so the energy of the system can be conserved in long time simulation It is guaranteed that the calculated values of the system dynamics parameters will be stable in long-time simulation. Discrete variational integrators based on Lie groups can guarantee the conservation of system geometry without adding constraints, and have high computational efficiency. The simulation results show that the energy, momentum and geometry of the 3D rigid body pendulum in geostationary orbit can be kept constant under the Lie group discrete variational integration algorithm.