Oscillator synthesis based on Nambu mechanics with canonical dissipative damping

Although circuit synthesis is one of the main subjects of circuit theory only a few systematic synthesis procedures are known for nonlinear circuits. Obviously, some of the difficulties for developing synthesis concepts for these circuits are related to theirs nonlinearities. In this paper we discuss a new mathematical concept for nonlinear differential equations that can be useful for the synthesis of a certain class of oscillator circuits. For this purpose we use Nambu mechanics where a system of differential equations can be constructed from a collection of invariants of movement (e.g. energy) and add a canonical dissipative damping term. It can be shown that the solution set of the system includes a stable limit cycle with prescribed properties. We illustrate our concept by means of an example.