Higher-Order Hamiltonian for Circuits with (alpha,beta) Elements
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Date
2020-04-05
Authors
Biolek, Zdeněk
Biolek, Dalibor
Biolková, Viera
Kolka, Zdeněk
0000-0002-7607-6146Advisor
Referee
Mark
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Volume Title
Publisher
MDPI AG
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Abstract
The paper studies the construction of the Hamiltonian for circuits built from the (alpha,beta) elements of Chua’s periodic table. It starts from the Lagrange function, whose existence is limited to sigma-circuits, i.e., circuits built exclusively from elements located on a common sigma-diagonal of the table. We show that the Hamiltonian can also be constructed via the generalized Tellegen’s theorem. According to the ideas of predictive modeling, the resulting Hamiltonian is made up exclusively of the constitutive relations of the elements in the circuit. Within the frame of Ostrogradsky’s formalism, the simulation scheme of S-circuits is designed and examined with the example of a nonlinear Pais–Uhlenbeck oscillator.
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Peer-reviewed
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en