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

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

Volume

21

Issue

1a

Volume

21

Issue

1a

Peer Reviewed

yes

Keywords

Poincaré-Cartan integral invariant, nonlinear constraints, nonholonomic, asynchronous variation, equations of motion, Poincare-Hamiltonian Systems.

Link to published version

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