Abstract
This paper begins by recalling how a constraint distribution on a configuration manifold induces a Dirac structure together with an implicit Lagrangian system, a construction that is valid even for degenerate Lagrangians. In such degenerate cases, it is shown in this paper that an implicit Hamiltonian system can be constructed by using a generalized Legendre transformation, where the primary constraints are incorporated into a generalized Hamiltonian on the Pontryagin bundle. Some examples of degenerate Lagrangians for L-C circuits, nonholonomic systems, and point vortices illustrate the theory.
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Yoshimura, H., Marsden, J.E. (2007). Dirac Structures and the Legendre Transformation for Implicit Lagrangian and Hamiltonian Systems. In: Allgüwer, F., et al. Lagrangian and Hamiltonian Methods for Nonlinear Control 2006. Lecture Notes in Control and Information Sciences, vol 366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73890-9_18
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DOI: https://doi.org/10.1007/978-3-540-73890-9_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73889-3
Online ISBN: 978-3-540-73890-9
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