Hamiltonian theory of constrained impulsive motion

Details Hamiltonian theory of constrained impulsive motion Hamiltonian theory of constrained impulsive motion

2004-01-27

arxiv.org/abs/math/0401380v1

Mathematics

Differential Geometry

36 pages, 4 figures

Scientific paper

This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions. Building on previous work on the Hamiltonian theory of impact, we tackle the problem of mathematically describing the classes of transitions that can occur. We propose a comprehensive formulation of the Transition Principle that encompasses the various impulsive regimes of Hamiltonian systems. Our formulation is based on the partial symplectic formalism, which provides a suitable framework for the dynamics of nonholonomic systems. We pay special attention to mechanical systems and illustrate the results with several examples.

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