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Dirac Structures and Implicit Lagrangian Systems in Electric Networks

Yoshimura, Hiroaki and Marsden, Jerrold E. (2006) Dirac Structures and Implicit Lagrangian Systems in Electric Networks. In: roceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems. , Kyoto, Japan, pp. 1444-1449.

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In this paper, we apply Dirac structures and the associated theory of implicit Lagrangian systems to electric networks. We show how a Dirac structure on the flux linkage phase can be induced from a KCL (Kirchhoff Current Law) constraint distribution on a configuration charge space in analogy with mechanics. In this context, a notion of implicit port-controlled Lagrangian systems is developed. As a specific illustrative example, it is demonstrated that a one-dimensional L-C transmission line can be formulated in the context of implicit port-controlled Lagrangian systems, where the transmission line may be regarded as an interconnected system of a chain of constituent primitive modules, each of which is given by an L-C circuit with external ports.

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Additional Information:The authors are grateful to Ehsan Afshari, who kindly gave several useful remarks. The research is partially supported by JSPS Grant 1650216 and in part by NSF-ITR Grant ACI-0204932.
Funding AgencyGrant Number
Japan Society for the Promotion of Science (JSPS)1650216
NSF - Information Technology Research (ITR)ACI-0204932
Subject Keywords:Implicit Lagrangian systems; Dirac structures; L-C transmission line
Record Number:CaltechAUTHORS:20101006-154047198
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20325
Deposited By: Tony Diaz
Deposited On:19 Nov 2010 23:26
Last Modified:26 Dec 2012 12:30

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