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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

Sebastián J. Ferraro 1, , David Iglesias-Ponte 2, and  D. Martín de Diego 3,

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.
Keywords: RATTLE method, holonomic and nonholonomic systems, energy-momentum integrators, variational integrators.
Mathematics Subject Classification: 37J60, 37M15, 70F25.
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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