Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A geometric Birkhoffian formalism for nonlinear RLC networks   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.

17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci