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Numerical and geometric aspects of the nonholonomic SHAKE and RATTLE methods

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  • 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.

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