A geometric Birkhoffian formalism for nonlinear RLC networks
| dc.creator | Ionescu, Delia | |
| dc.date | 2006-09-05 | |
| dc.date.accessioned | 2026-07-07T07:24:33Z | |
| dc.date.available | 2026-07-07T07:24:33Z | |
| dc.description | 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. | |
| dc.description | 30 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0609153 | |
| dc.identifier | http://arxiv.org/abs/math/0609153 | |
| dc.identifier | Journal of Geometry and Physics, 56(12), 2006 | |
| dc.identifier | doi:10.1016/j.geomphys.2006.01.007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116397 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Differential Geometry | |
| dc.subject | 34A26, 58A20, 94C | |
| dc.title | A geometric Birkhoffian formalism for nonlinear RLC networks | |
| dc.type | text |