  The aim of this paper is to give a formulation of the dynamics of nonlinear
RLC circuits as a geometric Birkhoffian system and to discuss in this context
the concepts of regularity, conservativeness, dissipativeness. An RLC circuit,
with no assumptions placed on its topology, will be described by a family of
Birkhoffian systems, parameterized by a finite number of real constants which
correspond to initial values of certain state variables of the circuit. The
configuration space and a special Pfaffian form, called Birkhoffian, are
obtained from the constitutive relations of the resistors, inductors and
capacitors involved and from Kirchhoff's laws. Under certain assumptions on the
voltage-current characteristic for resistors, it is shown that a Birkhoffian
system associated to an RLC circuit is dissipative. For RLC networks which
contain a number of pure capacitor loops or pure resistor loops the Birkhoffian
associated is never regular. A procedure to reduce the original configuration
space to a lower dimensional one, thereby regularizing the Birkhoffian, it is
also presented. In order to illustrate the results, specific examples are
discussed in detail.
