Algebroids and charge conservation

This paper presents two new choices of regular Lagrangians for the dynamical description of nonswitched LC networks, and proves that the solutions are equivalent to each other and to the results obtained in the literature. The first approach uses the integrated version of Kirchhoff's current law (topological constraints), which is just the condition of charge conservation, to define a regular Lagrangian description by using only the inductances of the system. The second approach is based on the formulation of a Lie algebroid which defines the constraints of the system in a different way. Both approaches are shown to be in a one-to-one relation and they both provide equivalent Hamiltonian formalisms.