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.
- Poincaré-Cartan integral invariant,
- nonlinear constraints,
- nonholonomic,
- asynchronous variation,
- equations of motion,
- Poincare-Hamiltonian Systems.
Available at: http://works.bepress.com/muhammad_usman/3/
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.
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