多刚体动力学仿真的李群变分积分算法

The configuration of rigid body can be described by its position vector and attitude matrix. The position vec⁃ tor can be accurately represented in a Euclidean space while the attitude matrix evolves on a Lie group. Due to the unique nonlinear properties of the Lie group，it’s difficult for the Euclidean space based modeling method and numeri⁃ cal algorithm to accurately capture the real dynamic characteristics of multibody systems，especially their long-time dy⁃ namic characteristics. Firstly，based on geometric mechanics theory，a Lie group variational integrator in the Hamilton system for simulating the multi-rigid body system dynamics is derived according to the discrete Hamilton’s principle and discrete Legendre transformation. Then，two different discrete forms of the Lie group variational integrator are further in⁃ troduced，namely，the general Lie group variational integrator and the RATTLie variational integrator. Finally，the two established discrete algorithms are respectively used to study the dynamics of a spatial double pendulum under the gravi⁃ ty action，and their characteristics，such as the group structure preservation and system energy conservation，are com⁃ paratively studied. Numerical results indicate that compared to the general Lie group algorithm，the RATTLie algorithm can achieve a higher computational accuracy，better group structure preservation and energy conservation.