Nonsmooth lagrangian mechanics and variational collision integrators

R. C. Fetecau, J. E. Marsden, M. Ortiz, M. West

Research output: Contribution to journalArticlepeer-review


Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions, and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Discretizations of this nonsmooth mechanics are developed by using the methodology of variational discrete mechanics. This leads to variational integrators which are symplectic-momentum preserving and are consistent with the jump conditions given in the continuous theory. Specific examples of these methods are tested numerically, and the long-time stable energy behavior typical of variational methods is demonstrated.

Original languageEnglish (US)
Pages (from-to)381-416
Number of pages36
JournalSIAM Journal on Applied Dynamical Systems
Issue number3
StatePublished - Aug 23 2003
Externally publishedYes


  • Collisions
  • Discrete mechanics
  • Variational integrators

ASJC Scopus subject areas

  • Analysis
  • Modeling and Simulation


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