Interconnection of Lagrange-Dirac dynamical systems for electric circuits

Henry Jacobs, Hiroaki Yoshimura, Jerrold E. Marsden

Research output: Contribution to journalConference article

3 Citations (Scopus)

Abstract

Previous constructions of Lagrangian mechanics for electric circuits have been found to diverge significantly from the standard Lagrangian mechanics of mechanical systems [1], [2]. The Lagrangian for a generic L-C circuit is degenerate, which prevents one from invoking the standard Euler-Lagrange equations [6]. Additionally, an interconnection of disconnected circuits places a Kirchhoff current constraint on the simultaneous dynamics of the two systems. This motivates us to develop the concept of interconnection for degenerate Lagrangian systems. Lagrange-Dirac Dynamical Systems (LDDS) have proven to be especially well suited for exactly such difficulties [8]. We provide a brief overview of LDDS following [6]. We then propose a means of interconnecting primitive subsystems by imposing an additional constraint. Finally, we demonstrate the interconnection theory by an example of L-C circuits.

Original languageEnglish
Pages (from-to)566-569
Number of pages4
JournalAIP Conference Proceedings
Volume1281
DOIs
Publication statusPublished - 2010 Dec 1
Externally publishedYes
EventInternational Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010 - Rhodes, Greece
Duration: 2010 Sep 192010 Sep 25

Keywords

  • Dirac Structures
  • Electric Circuits
  • Interconnection
  • Lagrange-Dirac Dynamical Systems

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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