Interconnection of Lagrange‐Dirac Dynamical Systems for Electric Circuits

Previous constructions of Lagrangian mechanics for electric circuits have been found to diverge significantly from the standard Lagrangian mechanics of mechanical systems [1], [2]. The Lagrangian for a generic L‐C circuit is degenerate, which prevents one from invoking the standard Euler‐Lagrange equations [6]. Additionally, an interconnection of disconnected circuits places a Kirchhoff current constraint on the simultaneous dynamics of the two systems. This motivates us to develop the concept of interconnection for degenerate Lagrangian systems. Lagrange‐Dirac Dynamical Systems (LDDS) have proven to be especially well suited for exactly such difficulties [8]. We provide a brief overview of LDDS following [6]. We then propose a means of interconnecting primitive subsystems by imposing an additional constraint. Finally, we demonstrate the interconnection theory by an example of L‐C circuits.