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Published 2010 | Published
Book Section - Chapter Open

Interconnection of Dirac Structures and Lagrange-Dirac Dynamical Systems

Abstract

In the paper, we develop an idea of interconnection of Dirac structures and their associated Lagrange- Dirac dynamical systems. First, we briefly review the Lagrange-Dirac dynamical systems (namely, implicit Lagrangian systems) associated to induced Dirac structures. Second, we describe an idea of interconnection of Dirac structures; namely, we show how two distinct Lagrange-Dirac systems can be interconnected through a Dirac structure on the product of configuration spaces. Third, we also show the variational structure of the interconnected Lagrange-Dirac dynamical system in the context of the Hamilton-Pontryagin-d'Alembert principle. Finally, we demonstrate our theory by an example of mass-spring mechanical systems.

Additional Information

© 2010. Research of HY is partially supported by JSPS Grant-in Aid 20560229, JST-CREST and Waseda University Grant for SR 2010A-606; Research of JEM is partially supported by NSF grant DMS-0505711.

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