Multibody System Dynamics

, Volume 39, Issue 3, pp 267–290 | Cite as

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

Article

Abstract

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.

Keywords

Baumgarte stabilization Frictional unilateral constraints Differential algebraic inclusions 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Kyushu UniversityFukuokaJapan
  2. 2.INRIA Grenoble Rhônes-AlpesSaint-IsmierFrance

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