Hamilton’s Principle for Circuits with Dissipative Elements

Biolek, Zdeněk; Biolek, Dalibor; Biolková, Viera

doi:10.1155/2019/2035324

Cited by 2 publications

(2 citation statements)

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“…In order to apply the Lagrange formalism to circuits with HOEs, the transform between these two sets of variables must be used. The following procedure is a generalization of the method described in [19]. Consider the above transform as a linear combination of the variables x i…”

Section: Lawmentioning

confidence: 99%

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Lagrangian for Circuits with Higher-Order Elements

Biolek

Biolková

2019

Entropy

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The necessary and sufficient conditions of the validity of Hamilton’s variational principle for circuits consisting of (α,β) elements from Chua’s periodical table are derived. It is shown that the principle holds if and only if all the circuit elements lie on the so-called Σ-diagonal with a constant sum of the indices α and β. In this case, the Lagrangian is the sum of the state functions of the elements of the L or +R types minus the sum of the state functions of the elements of the C or −R types. The equations of motion generated by this Lagrangian are always of even-order. If all the elements are linear, the equations of motion contain only even-order derivatives of the independent variable. Conclusions are illustrated on an example of the synthesis of the Pais–Uhlenbeck oscillator via the elements from Chua’s table.

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Section: Lawmentioning

confidence: 99%

“…Since no other HOEs, the negative resistors being among them, are missing in Wang's table, this table cannot be utilized for our purposes. It is well documented via the impossibility of drawing a Lagrangian for circuits with dissipative elements [19].…”

Section: Introductionmentioning

confidence: 99%