%0 Journal Article
%T Lagrangian for Circuits with Higher-Order Elements
%J Entropy | An Open Access Journal from MDPI
%D 2019
%R https://doi.org/10.3390/e21111059
%X The necessary and sufficient conditions of the validity of Hamilton¡¯s variational principle for circuits consisting of (¦Á,¦Â) 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 ¦²-diagonal with a constant sum of the indices ¦Á and ¦Â. 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¨CUhlenbeck oscillator via the elements from Chua¡¯s table. View Full-Tex
%U https://www.mdpi.com/1099-4300/21/11/1059