The necessary and sufficient conditions of the validity of Hamilton’s variational principle for circuits consisting of (α
) 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
. In this case, the Lagrangian is the sum of the state functions of the elements of the L
types minus the sum of the state functions of the elements of the C
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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