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Article
A Generalization of Poincaré-Cartan Integral Invariants of a Nonlinear Nonholonomic Dynamical System
Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
  • Muhammad Usman, University of Dayton
  • M. Imran, Quaid-I-Azam University, Islama bad, Pakistan
Document Type
Article
Publication Date
1-1-2014
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
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.

Publisher
Watam press
Peer Reviewed
Yes
Keywords
  • Poincaré-Cartan integral invariant,
  • nonlinear constraints,
  • nonholonomic,
  • asynchronous variation,
  • equations of motion,
  • Poincare-Hamiltonian Systems.
Citation Information
Muhammad Usman and M. Imran. "A Generalization of Poincaré-Cartan Integral Invariants of a Nonlinear Nonholonomic Dynamical System" Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis Vol. 21 Iss. 1a (2014)
Available at: http://works.bepress.com/muhammad_usman/3/