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Published 2007 | public
Book Section - Chapter

Dirac structures and the Legendre transformation for implicit Lagrangian and Hamiltonian systems

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.

Additional Information

© Springer-Verlag Berlin Heidelberg 2007. This research was partially supported by JSPS Grant 16560216 and NSF-ITR Grant ACI-0204932.

Additional details

Created:
August 19, 2023
Modified:
January 13, 2024