Abstract

The interest on closed-form analytical sensitivity equations based on the classical forward dynamics formulations, started shortly after the equations were ready and became popular. A vast effort was devoted by the authors in the last years to derive the forward and adjoint sensitivity equations for some state-of-the-art formulations of practical interest. Recently, the forward sensitivity equations for the index-3 augmented Lagrangian formulation with projections (the ALI3-P formulation) have been derived. In this article, the ALI3-P adjoint sensitivity equations are derived and implemented in the MBSLIM library as a general code and tested in one academic example and one real-life multibody system.

摘要

对基于经典正向动力学公式的封闭式分析灵敏度方程的兴趣始于方程准备好并流行起来后不久。在过去几年中，作者付出了巨大的努力来推导出一些具有实际意义的最新公式的前向和伴随灵敏度方程。最近，已经导出了具有投影的指数 3 增强拉格朗日公式（ALI3-P 公式）的前向灵敏度方程。在本文中，ALI3-P 伴随灵敏度方程作为通用代码在 MBSLIM 库中导出和实现，并在一个学术示例和一个现实生活中的多体系统中进行了测试。