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2003•IEEE Transactions on Circuits and Systems I Fundamental Theory and ApplicationsOpen access

Relating lagrangian and hamiltonian formalisms of LC circuits

Jesús Clemente-Gallardo, Jacquelien M.A. Scherpen

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Abstract

The Lagrangian formalism defined by Scherpen et al. (2000) for (switching) electrical circuits, is adapted to the Lagrangian formalism defined on Lie algebroids. This allows us to define regular Lagrangians and consequently, well-defined Hamiltonian descriptions of arbitrary LC networks. The relation with other Hamiltonian approaches is also analyzed and interpreted.

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The Lagrangian formalism defined by Scherpen et al. (2000) for (switching) electrical circuits, is adapted to the Lagrangian formalism defined on Lie algebroids. This allows us to define regular Lagrangians and consequently, well-defined Hamiltonian descriptions of arbitrary LC networks. The relation with other Hamiltonian approaches is also analyzed and interpreted.

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Available abstract

The Lagrangian formalism defined by Scherpen et al. (2000) for (switching) electrical circuits, is adapted to the Lagrangian formalism defined on Lie algebroids. This allows us to define regular Lagrangians and consequently, well-defined Hamiltonian descriptions of arbitrary LC networks. The relation with other Hamiltonian approaches is also analyzed and interpreted.

Key concepts: Rotation formalisms in three dimensions, Lagrangian, Hamiltonian (control theory), Formalism (music), Electronic circuit, Hamiltonian formalism, Covariant Hamiltonian field theory, Mathematics

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