基于重心插值的多体系统动力学离散变分方法

Discrete Variational Method of Multi-body System Dynamics Cased on Center of Gravity Interpolation

针对多体系统动力学仿真欧拉—拉格朗日方程的数值求解,基于哈密顿原理和离散变分原理的方法,以平面双连杆为数值算例,使用插值方法和数值积分得到其离散的欧拉—拉格朗日方程,对该离散方程进行求解。离散过程采用重心拉格朗日插值提高算法稳定性,插值节点分别选取等距节点和非均匀节点,其中非均匀节点包括第一类、第二类Chebyshev节点,数值积分采用精度较高的高斯勒让德积分。数值结果表明,该方法在步长较大时相比传统采用的龙格库塔法得到较好的结果,并且具有更高的效率,适用于长时间仿真。

For the numerical solution of Euler -Lagrange equation of multi-body system dynamics simula-tion, the paper proposed the method that based on Hamiltonian principle and discrete variational principle. With the example of planar two-link, the paper got the discrete Euler-Lagrange equation by using the in-terpolation method and numerial integral. To improve the stability, this paper takes the use of the center of gravity Lagrange interpolation by using equidistant nodes and heterogeneous nodes which include the first and second Chebyshev nodes. The high-precision Gauss Legendre integral is used during the integra-tion procedure. It can be seen from the results, this method is applicable for the simulation of long time due to the better calculation results than Runge-Kutta method with higher efficiency in large step.