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Γ-convergence of Variational Integrators for Constrained Systems

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Abstract

For a physical system described by a motion in an energy landscape under holonomic constraints, we study the Γ-convergence of variational integrators to the corresponding continuum action functional and the convergence properties of solutions of the discrete Euler–Lagrange equations to stationary points of the continuum problem. This extends the results in Müller and Ortiz (J. Nonlinear Sci. 14:279–296, 2004) to constrained systems. The convergence result is illustrated with examples of mass point systems and flexible multibody dynamics.

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Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85747, Garching, Germany

    Bernd Schmidt

  2. Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA, 91125, USA

    Sigrid Leyendecker & Michael Ortiz

Authors
  1. Bernd Schmidt
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  2. Sigrid Leyendecker
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  3. Michael Ortiz
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Correspondence to Bernd Schmidt.

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Communicated by Robert V. Kohn.

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Schmidt, B., Leyendecker, S. & Ortiz, M. Γ-convergence of Variational Integrators for Constrained Systems. J Nonlinear Sci 19, 153–177 (2009). https://doi.org/10.1007/s00332-008-9030-1

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  • DOI: https://doi.org/10.1007/s00332-008-9030-1

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