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2009, Volume 2009: 220-229. Doi: 10.3934/proc.2009.2009.220 open access
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Numerical and geometric aspects of the nonholonomic SHAKE and RATTLE methods

  • 1.

    Departamento de Mateemática and Instituto de Matemática Bahía Blanca, Universidad Nacional del Sur, Av. Alem 1253, 8000 Bahía Blanca and CONICET

  • 2.

    Unidad asociada ULL-CSIC “Geometría Diferencial y Mecánica Geométrica”, Departamento de Matemática Fundamental, Facultad de Matemáticas, Universidad de la Laguna, La Laguna, Tenerife, Canary Islands

  • 3.

    Unidad Asociada ULL-CSIC Geometría Diferencial y Mecánica Geométrica, Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Serrano 123, 28006 Madrid

Received:  August 2008
Revised:  April 2009
Published:  August 2009
Abstract Related Papers Cited by
    Abstract
  • Here we discuss a geometric integrator for nonholonomic mechanical systems that preserves the nonholonomic constraints, the discrete nonholonomic momentum map, and is also energy-preserving in some important cases. This method does not require a predefined discretization of the nonholonomic constraints. In Euclidean space, it yields a generalization of the classical SHAKE and RATTLE algorithms to the nonholonomic setting. This article shows that the method is second order convergent.
    Mathematics Subject Classification: 37J60, 37M15, 70F25.

    Citation:
    shu

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