Integrability and the variational formulation of non-conservative mechanical systems
Version of Record online: 21 JAN 2009
Copyright © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Annalen der Physik
Volume 18, Issue 1, pages 45–56, February 2009
How to Cite
Delphenich, D.H. (2009), Integrability and the variational formulation of non-conservative mechanical systems. Ann. Phys., 18: 45–56. doi: 10.1002/andp.200710332
- Issue online: 21 JAN 2009
- Version of Record online: 21 JAN 2009
- Manuscript Accepted: 28 NOV 2008
- Manuscript Revised: 27 NOV 2008
- Manuscript Received: 29 AUG 2007
- Variational mechanics;
- non-conservative systems;
- integrability of jets.
It is shown that one can obtain canonically-defined dynamical equations for non-conservative mechanical systems by starting with a first variation functional, instead of an action functional, and finding their zeroes. The kernel of the first variation functional, as an integral functional, is a 1-form on the manifold of kinematical states, which then represents the dynamical state of the system. If the 1-form is exact then the first variation functional is associated with the first variation of an action functional in the usual manner. The dynamical equations then follow from the vanishing of the dual of the Spencer operator that acts on the dynamical state. This operator, in turn, relates to the integrability of the kinematical states. The method is applied to the modeling of damped oscillators.