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. http://resolver.caltech.edu/CaltechAUTHORS:20101006-154047198
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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.
|Item Type:||Book Section|
|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.|
|Subject Keywords:||Implicit Lagrangian systems; Dirac structures; L-C transmission line|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||19 Nov 2010 23:26|
|Last Modified:||26 Dec 2012 12:30|
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