Title
A Generalization of Poincaré-Cartan Integral Invariants of a Nonlinear Nonholonomic Dynamical System
Document Type
Article
Publication Date
2014
Publication Source
Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Abstract
Based on the d'Alembert-Lagrange-Poincar\'{e} variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We write these equations in a canonical form called the Poincar\'{e}-Hamilton equations, and study a version of corresponding Poincar\'{e}-Cartan integral invariant which are derived by means of a type of asynchronous variation of the Poincar\'{e} variables of the problem that involve the variation of the time. As a consequence, it is shown that the invariance of a certain line integral under the motion of a mechanical system of the type considered characterizes the Poincar\'{e}-Hamilton equations as underlying equations of the motion. As a special case, an invariant analogous to Poincar\'{e} linear integral invariant is obtained.
Inclusive pages
111-134
Document Version
Postprint
Copyright
Copyright © 2014, Watam Press.
Publisher
Watam press
Volume
21
Issue
1a
Peer Reviewed
yes
Keywords
Poincaré-Cartan integral invariant, nonlinear constraints, nonholonomic, asynchronous variation, equations of motion, Poincare-Hamiltonian Systems.
eCommons Citation
Usman, Muhammad and Imran, M., "A Generalization of Poincaré-Cartan Integral Invariants of a Nonlinear Nonholonomic Dynamical System" (2014). Mathematics Faculty Publications. 3.
https://ecommons.udayton.edu/mth_fac_pub/3
Comments
The paper available for download is the authors' final manuscript, accepted for publication in the journal Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis. Some differences may exist between this version and the published version, which is available online.
Permission documentation is on file.