An intrinsic Hamiltonian formulation of the dynamics of LC-circuits


Maschke, B.M. and Schaft, A.J. van der and Breedveld, P.C. (1995) An intrinsic Hamiltonian formulation of the dynamics of LC-circuits. IEEE Transactions on Circuits and Systems I: Fundamental theory and applications, 42 (2). pp. 73-82. ISSN 1057-7122

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Abstract:First, the dynamics of LC-circuits are formulated as a Hamiltonian system defined with respect to a Poisson bracket which may be degenerate, i.e., nonsymplectic. This Poisson bracket is deduced from the network graph of the circuit and captures the dynamic invariants due to Kirchhoff's laws. Second, the antisymmetric relations defining the Poisson bracket are realized as a physical network using the gyrator element and partially dualizing the network graph constraints. From the network realization of the Poisson bracket, the reduced standard Hamiltonian system as well as the realization of the embedding standard Hamiltonian system are deduced
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Copyright:© 1995 IEEE
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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