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. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Yoshimura, H., & Marsden, J. E. (2007). Dirac structures and the legendre transformation for implicit lagrangian and hamiltonian systems. In Lecture Notes in Control and Information Sciences (Vol. 366 LNCIS, pp. 233–247). Springer Verlag. https://doi.org/10.1007/978-3-540-73890-9_18
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