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  1. Zeitschrift für angewandte Mathematik und Physik
  2. Zeitschrift für angewandte Mathematik und Physik : Volume 58
  3. Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 2, March 2007
  4. Birkhoffian formulation of the dynamics of LC circuits
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Zeitschrift für angewandte Mathematik und Physik : Volume 67
Zeitschrift für angewandte Mathematik und Physik : Volume 66
Zeitschrift für angewandte Mathematik und Physik : Volume 65
Zeitschrift für angewandte Mathematik und Physik : Volume 64
Zeitschrift für angewandte Mathematik und Physik : Volume 63
Zeitschrift für angewandte Mathematik und Physik : Volume 62
Zeitschrift für angewandte Mathematik und Physik : Volume 61
Zeitschrift für angewandte Mathematik und Physik : Volume 60
Zeitschrift für angewandte Mathematik und Physik : Volume 59
Zeitschrift für angewandte Mathematik und Physik : Volume 58
Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 6, November 2007
Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 5, September 2007
Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 4, July 2007
Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 3, May 2007
Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 2, March 2007
Birkhoffian formulation of the dynamics of LC circuits
On the irrotational approximation to steady supersonic flow
Eigenvalue estimates and critical temperature in zero fields for enhanced surface superconductivity
Dynamics of a thermoelastic von Kármán plate in a subsonic gas flow
Some solutions (linear in the spatial variables) and generalized Chapman–Enskog functions basic to the linearized Boltzmann equations for a binary mixture of rigid spheres
On the bidirectional vortex and other similarity solutions in spherical coordinates
The elasticity of elasticity
A revisit to the bending problem of a thin elliptic aelotropic plate with simply supported edge and uniform lateral load
On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack
A convergence result for spatially inhomogeneous Preisach operators
Zeitschrift für angewandte Mathematik und Physik : Volume 58, Issue 1, January 2007
Zeitschrift für angewandte Mathematik und Physik : Volume 57
Zeitschrift für angewandte Mathematik und Physik : Volume 56
Zeitschrift für angewandte Mathematik und Physik : Volume 55
Zeitschrift für angewandte Mathematik und Physik : Volume 54
Zeitschrift für angewandte Mathematik und Physik : Volume 53
Zeitschrift für angewandte Mathematik und Physik : Volume 52
Zeitschrift für angewandte Mathematik und Physik : Volume 51
Zeitschrift für angewandte Mathematik und Physik : Volume 50
Zeitschrift für angewandte Mathematik und Physik : Volume 49
Zeitschrift für angewandte Mathematik und Physik : Volume 48

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Birkhoffian formulation of the dynamics of LC circuits

Content Provider SpringerLink
Author Ionescu, Delia Scheurle, Jürgen
Copyright Year 2006
Abstract We present a formulation of general nonlinear LC circuits within the framework of Birkhoffian dynamical systems on manifolds. We develop a systematic procedure which allows, under rather mild non-degeneracy conditions, to write the governing equations for the mathematical description of the dynamics of an LC circuit as a Birkhoffian differential system. In order to illustrate the advantages of this approach compared to known Lagrangian or Hamiltonian approaches we discuss a number of specific examples. In particular, the Birkhoffian approach includes networks which contain closed loops formed by capacitors, as well as inductor cutsets. We also extend our approach to the case of networks which contain independent voltage sources as well as independent current sources. Also, we derive a general balance law for an associated “energy function”.
Starting Page 175
Ending Page 208
Page Count 34
File Format PDF
ISSN 00442275
Journal Zeitschrift für angewandte Mathematik und Physik
Volume Number 58
Issue Number 2
e-ISSN 14209039
Language English
Publisher Birkhäuser-Verlag
Publisher Date 2006-12-18
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Conservative dynamical systems Birkhoffian differential systems Birkhoffian vector fields electrical networks geometric theory Theoretical and Applied Mechanics Mathematical Methods in Physics
Content Type Text
Resource Type Article
Subject Applied Mathematics Physics and Astronomy
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