The University of Southampton
University of Southampton Institutional Repository

# Some generalized variational principles for conservative holonomic dynamical systems

Xing, Jing-Tang and Price, W.G. (1992) Some generalized variational principles for conservative holonomic dynamical systems. Proceedings of the Royal Society: Mathematical and Physical Sciences, 436 (1897), 331-344.

Record type: Article

## Abstract

For four types of time boundary conditions, some generalized variational principles for conservative holonomic dynamical systems are developed. The traditional Hamilton's principle and its second form as well as Toupin's principle are special cases of the general principles given in this paper. The generalized principles provide several analytical approaches to study dynamical systems formulated in the following spaces: (q$_{i}$, t), (p$_{i}$, t), (q$_{i}$, p$_{i}$, t), (q$_{i}$, v$_{i}$, p$_{i}$, t), (q$_{i}$, Q$_{i}$, p$_{i}$, t) and (q$_{i}$, v$_{i}$, Q$_{i}$, p$_{i}$, t) where q$_{i}$ represents the generalized coordinate, p$_{i}$ the generalized momentum, Q$_{i}$ the generalized force and v$_{i}$ the generalized velocity. In the paper the second form of Hamilton's principle as stated by F. R. Gantmacher is discussed. From the accompanying analysis, new principles are developed and the principal paths as well as the alternative side paths corresponding to these new forms are illustrated and compared with the one originally presented by F. R. Gantmacher.

Full text not available from this repository.

Published date: 1992
Additional Information: Cited by International Aerospace Abstracts A92-25346, vol.32(9),1992

## Identifiers

Local EPrints ID: 22147
URI: http://eprints.soton.ac.uk/id/eprint/22147
ISSN: 0962-8444
PURE UUID: 8d473e15-96f7-4e72-8c47-74a3c3857a1f

## Catalogue record

Date deposited: 30 Jan 2007

## Contributors

Author: Jing-Tang Xing
Author: W.G. Price