Conference abstracts

Session A5 - Geometric Integration and Computational Mechanics

July 11, 15:30 ~ 16:00 - Room 111

How do nonholonomic integrators work?

Olivier Verdier

Western Norway University of Applied Sciences, Norway   -

Nonholonomic systems are mechanical systems with constraints on the velocity. Their behaviour is quite different from that of mechanical systems with constraints on the positions (holonomic systems). There has been reports in the literature of integrators which behaved particularly well for some nonholonomic systems: near conservation of energy, or near conservation of other integrals.

We will explain the general mechanism behind those good properties. The main structure of the examples where the nonholonomic integrators work is that of a fibration over a reversible integrable system. The explaining theory, for descending integrators, is then the reversible Kolmogorov–Arnold–Moser theory.

We will explain how to design various systems which deviate from that pattern, in order to show experimentally that this structure of fibration over a reversible integrable system is necessary. Non-holonomic integrators do not preserve any of the features of those perturbed systems: neither the energy, nor the integrable structure.

We will also single out one non-holonomic integrator, which has two properties of interests: it is semi-implicit for a large range of systems, and it still has a good, completely unexplained, behaviour on some nonholonomic systems.

Joint work with Klas Modin (Chalmers University of Technology).

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