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2009, 2009(Special): 220-229. doi: 10.3934/proc.2009.2009.220

## 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, Argentina 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, Spain 3 Unidad Asociada ULL-CSIC Geometría Diferencial y Mecánica Geométrica, Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Serrano 123, 28006 Madrid, Spain

Received  August 2008 Revised  April 2009 Published  September 2009

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.
Citation: Sebastián J. Ferraro, David Iglesias-Ponte, D. Martín de Diego. Numerical and geometric aspects of the nonholonomic SHAKE and RATTLE methods. Conference Publications, 2009, 2009 (Special) : 220-229. doi: 10.3934/proc.2009.2009.220
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