Momentum and energy preserving integrators for nonholonomic dynamics

Abstract

In this paper, we propose a geometric integrator for nonholonomic mechanical systems. It can be applied to discrete Lagrangian systems specified through a discrete Lagrangian defined on QxQ, where Q is the configuration manifold, and a (generally nonintegrable) distribution in TQ. In the proposed method, a discretization of the constraints is not required. We show that the method preserves the discrete nonholonomic momentum map, and also that the nonholonomic constraints are preserved in average. We study in particular the case where Q has a Lie group structure and the discrete Lagrangian and/or nonholonomic constraints have various invariance properties, and show that the method is also energy-preserving in some important cases.

arXiv comment18 pages, 6 figures; v2: example and figures added, minor correction to example 2; v3: added section on nonholonomic Stoermer-Verlet method

References in corpus (6)

• Discrete Euler-Poincaré and Lie-Poisson Equations
• Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top
• Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids
• Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
• Discrete Nonholonomic LL Systems on Lie Groups
• A Generalization of Chetaev's Principle for a Class of Higher Order Non-holonomic Constraints

Cited by in corpus (7)

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• What makes nonholonomic integrators work?
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• Feedback Integrators for Nonholonomic Mechanical Systems
• The inverse problem of the calculus of variations for discrete systems
• Variational approach to nonholonomic and inequality-constrained mechanics
• Variational order for forced Lagrangian systems II: Euler-Poincaré equations with forcing