平面刚体系统的参数预调节保辛算法

保辛积分方法在约束哈密顿系统中有着重要的应用，是因为其在长时间仿真中表现出极好的稳定性。然而随着仿真时长增加，保辛格式通常具有较大的相位误差累积。本文提出了一种平面多刚体系统的参数预调节保辛积分方法。通过推导具有待定参数的改进的拉格朗日方程，并将其与已有保辛格式相结合并预先调节相关参数取值，可以大幅降低数值解的相位误差。理论分析与数值结果表明参数预调节保辛积分方法不仅保持了辛结构，而且具有很低的相位误差累积。因此，参数预调节保辛积分方法可应用于长时间仿真分析。

A parameter-preadjusted symplectic algorithm for planar rigid body systems

Symplectic integrations have important applications for constrained Hamiltonian systems because they exhibit excellent stability in long-time simulations.However, the symplectic scheme usually has a large phase error accumulation with the increase of simulation time.This paper develops a parameter-preadjusted symplectic integration for planar rigid multibody systems with Cartesian coordinates.By deriving the modified Lagrangian equation with undetermined parameters, combining it with the existing symplectic scheme, and adjusting the corresponding parameter in advance, the symplectic method can greatly reduce the phase error of the numerical solution.Theoretical analysis and numerical results show that the new method not only preserves the symplectic structure of the flow but also presents a very low phase error accumulation.Therefore, the parameter-preadjusted symplectic integration is recommended for long-time simulations.