基于Hermite 插值的多体系统动力学离散变分方法

针对多体系统动力学数值仿真问题,研究基于Hermite插值的离散变分方法.首先对广义坐标和广义速度进行Hermite插值,结合Gauss数值积分方法,利用Hamilton原理和离散力学变分原理,建立了含已知导数信息和含未知导数信息的Hermite插值离散变分数学模型,求解得到精确度较高的动力学仿真结果.该方法可以在步长较大时精确保持约束方程,并保持系统总能量在一定范围内有界变化,适用于长时间仿真情况.

Discrete variational method of multibody system dynamics based on hermite interpolation

The discrete variational method based on Hermite interpolation is studied for the simulation problem of multibody system dynamics. Hermite interpolation is carried out to interpolate the generalized coordinate and the generalized velocity, firstly. Then, using the Gauss numerical integral method, the Hamilton principle and discrete variational principles of mechanics, the discrete variational mathematical model based on the Hermite interpolation containing known and unknown derivative information is established. High accuracy simulation results is obtained by solving the presented discrete variational equations. This method can accurately maintain the constraint equations on the larger time step, and keep the total energy of the system in a certain range of bounded variation. Therefore, it can be applied for the long time simulation. © 2018 Journal of Dynamics and Control. All rights reserved.