On the variational formulation of systems with non-holonomic constraints

Details On the variational formulation of systems with non-holonomic constraints On the variational formulation of systems with non-holonomic constraints

2009-08-13

arxiv.org/abs/0908.1950v1

Ann. Phys. (Berlin) 18 (2009), 1-22

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, 1 figure

Scientific paper

In a previous article by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems by starting with the first variation functional instead of an action functional. In this article, it is shown that this same approach will also allow one to give a variational formulation to systems with non-holonomic constraints. The key is to use an adapted anholonomic local frame field in the formulation, which then implies the replacement of ordinary derivatives with covariant ones. The method is then applied to the case of a vertical disc rolling without slipping or friction on a plane.

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