On the variational formulation of systems with non-holonomic constraints
Article first published online: 17 AUG 2009
Copyright © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Annalen der Physik
Volume 18, Issue 9, pages 649–670, September 2009
How to Cite
Delphenich, D.H. (2009), On the variational formulation of systems with non-holonomic constraints. Ann. Phys., 18: 649–670. doi: 10.1002/andp.200910364
- Issue published online: 17 AUG 2009
- Article first published online: 17 AUG 2009
- Manuscript Accepted: 15 JUL 2009
- Manuscript Received: 22 JUN 2009
- Variational mechanics;
- non-holonomic constraints;
- integrability of jets.
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.