A new representation of systems with frictional unilateral constraints and its Baumgarte-like relaxation

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• 作者：Ryo Kikuuwe ; Bernard Brogliato
• 关键词：Baumgarte stabilization ; Frictional unilateral constraints ; Differential algebraic inclusions
• 刊名：Multibody System Dynamics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：39
• 期：3
• 页码：267-290
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Optimization; Electrical Engineering; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-272X
• 卷排序：39

文摘

This paper proposes a new representation of multibody mechanical systems involving three-dimensional frictional unilateral constraints. The new representation is of the form of a differential algebraic inclusion (DAI) employing a normal cone with a non-Euclidean, singular norm metric. It can be seen as a generalization of a differential algebraic equation (DAE) using Lagrange multipliers, which has been used to represent mechanical systems with equality constraints. The paper also presents an approach to approximate the aforementioned DAI by another form of DAI, which can be equivalently converted into an ordinary differential equation (ODE). The approach can be seen as a generalization of the Baumgarte stabilization, which was originally developed for DAEs. The new DAI representation and its ODE approximation are illustrated with some simple examples.