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.