1 research outputs found
Momentum and energy preserving integrators for nonholonomic dynamics
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.Comment: 18 pages, 6 figures; v2: example and figures added, minor correction
to example 2; v3: added section on nonholonomic Stoermer-Verlet metho