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Interconnection of Dirac Structures and Lagrange-Dirac Dynamical Systems

Yoshimura, Hiroaki and Jacobs, Henry and Marsden, Jerrold E. (2010) Interconnection of Dirac Structures and Lagrange-Dirac Dynamical Systems. In: Proceedings of Mathematical Theory of Networks and Systems (MTNS 2010), Budapest, Hungary, 5-9 July, 2010. MTNS , Blacksburg, VA, pp. 247-252. ISBN 9789633113707.

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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.

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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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JSPS grant-in-aid20560229
JST-CREST/Waseda UniversitySR 2010A-606
Record Number:CaltechAUTHORS:20101026-080012143
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20520
Deposited By: Ruth Sustaita
Deposited On:30 Nov 2010 19:00
Last Modified:03 Oct 2019 02:11

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