Interconnection of Lagrange-Dirac dynamical systems for electric circuits

Henry Jacobs, Hiroaki Yoshimura, Jerrold E. Marsden

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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
Title of host publicationAIP Conference Proceedings
Pages566-569
Number of pages4
Volume1281
DOIs
Publication statusPublished - 2010
Externally publishedYes
EventInternational Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010 - Rhodes, Greece
Duration: 2010 Sep 192010 Sep 25

Other

OtherInternational Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010
CountryGreece
CityRhodes
Period10/9/1910/9/25

Fingerprint

dynamical systems
Euler-Lagrange equation

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Jacobs, H., Yoshimura, H., & Marsden, J. E. (2010). Interconnection of Lagrange-Dirac dynamical systems for electric circuits. In AIP Conference Proceedings (Vol. 1281, pp. 566-569) https://doi.org/10.1063/1.3498539

Interconnection of Lagrange-Dirac dynamical systems for electric circuits. / Jacobs, Henry; Yoshimura, Hiroaki; Marsden, Jerrold E.

AIP Conference Proceedings. Vol. 1281 2010. p. 566-569.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Jacobs, H, Yoshimura, H & Marsden, JE 2010, Interconnection of Lagrange-Dirac dynamical systems for electric circuits. in AIP Conference Proceedings. vol. 1281, pp. 566-569, International Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010, Rhodes, Greece, 10/9/19. https://doi.org/10.1063/1.3498539
Jacobs H, Yoshimura H, Marsden JE. Interconnection of Lagrange-Dirac dynamical systems for electric circuits. In AIP Conference Proceedings. Vol. 1281. 2010. p. 566-569 https://doi.org/10.1063/1.3498539
Jacobs, Henry ; Yoshimura, Hiroaki ; Marsden, Jerrold E. / Interconnection of Lagrange-Dirac dynamical systems for electric circuits. AIP Conference Proceedings. Vol. 1281 2010. pp. 566-569
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