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

Ryo Kikuuwe, Bernard Brogliato

Research output: Contribution to journalArticle

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)267-290
Number of pages24
JournalMultibody System Dynamics
Issue number3
Publication statusPublished - Mar 1 2017


All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Aerospace Engineering
  • Mechanical Engineering
  • Computer Science Applications
  • Control and Optimization

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