非光滑机械系统仿真与控制的逆向误差分析方法

David Pekarek, T. Murphey
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引用次数: 6

摘要

本文提出了受单边约束弹性冲击的拉格朗日系统的一种原始的结构化积分方案。在推导该方法时,使用修正系统哈密顿量的概念,采用反向误差分析方法建立了碰撞的离散时间守恒律。本文从分析和仿真两方面论证了不采用该守恒律的现有仿真方法的不足。与这些方法相比,我们的方案在离散时间能量行为、轨迹精度和方法精度的一致顺序方面具有优势。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A backwards error analysis approach for simulation and control of nonsmooth mechanical systems
This paper presents an original structured integration scheme for Lagrangian systems undergoing elastic impacts due to unilateral constraints. In deriving the method, a backwards error analysis approach establishes a discrete time conservation law for impacts using the notion of a modified system Hamiltonian. Shortcomings of existing simulation methods that do not use this conservation law are demonstrated both analytically and in simulation. Relative to these methods, our scheme provides advantages in terms of discrete time energy behavior, accuracy of trajectories, and consistent order of accuracy of the method.
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