Numerical and geometric aspects of the nonholonomic SHAKE and RATTLE methods

SEBASTIÁN J. FERRARO; DAVID IGLESIAS-PONTE; DAVID MARTÍN DE DIEGO

Arlington, TX

Congreso; 7th AIMS International Conference on Dynamical Systems, Differential Equations and Applications; 2008

American Institute of Mathematical Sciences

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.