Hamilton's Principle for Circuits with Dissipative Elements

The classic form of Hamilton’s variational principle does not hold for circuits with dissipative elements. It is shown in the paper that this may not be true in the case of systems consisting of the so-called higher-order elements. Hamilton’s principle is then extended to circuits containing the classical resistors and Frequency Dependent Negative Resistors (FDNRs). The extension is also made to any pair of elements which are the nearest neighbours on any - diagonal of Chua’s table.

[1]  Dalibor Biolek,et al.  (Co)content in Circuits With Memristive Elements , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Leon O. Chua,et al.  Device modeling via nonlinear circuit elements , 1980 .

[3]  Dalibor Biolek,et al.  Taxicab geometry in table of higher-order elements , 2019, Nonlinear Dynamics.

[4]  Riewe,et al.  Nonconservative Lagrangian and Hamiltonian mechanics. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Leonard T. Bruton.  Frequency selectivity using positive impedance converter-type networks , 1968 .

[6]  Peter G. Bergmann,et al.  Principles of Relativity Physics , 1967 .

[7]  L. Chua.  Memristor-The missing circuit element , 1971 .

[8]  Dalibor Biolek,et al.  Nonlinear inerter in the light of Chua's table of higher-order electrical elements , 2016, 2016 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS).

[9]  Dalibor Biolek,et al.  Duality of Complex Systems Built from Higher-Order Elements , 2018, Complex..

[10]  Malcolm C. Smith.  Synthesis of mechanical networks: the inerter , 2002, IEEE Trans. Autom. Control..

[11]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

[12]  Dalibor Biolek,et al.  Euler-Lagrange Equations of Networks with Higher-Order Elements , 2017 .