Numerical and geometric aspects of the nonholonomic SHAKE and RATTLE methods
Sebastián J. Ferraro - Departamento de Mateemática and Instituto de Matemática Bahía Blanca, Universidad Nacional del Sur, Av. Alem 1253, 8000 Bahía Blanca and CONICET, Argentina (email)
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.
Keywords: RATTLE method, holonomic and nonholonomic systems, variational integrators, energy-momentum integrators
Received: August 2008; Revised: April 2009; Published: September 2009.