An intrinsic Hamiltonian formulation of network dynamics: Non-standard Poisson structures and gyrators
type: Item
instance of: scholarly article
title: An intrinsic Hamiltonian formulation of network dynamics: Non-standard Poisson structures and gyrators
zbMATH Open document ID: 0807.70015
DOI: 10.1016/S0016-0032(92)90049-M
published in: Journal of the Franklin Institute
publication date: 1994-03-22T00:00:00Z
review text: This paper gives an intrinsic Hamiltonian formulation in the context of Poisson manifolds of equations of motion in network models of nonresistive systems. Many examples and references are given to illustrate a general theory. The latter, however, is never formulated (in my opinion) in a truly explicit general way. The paper begins with a survey of basic known results on Poisson manifolds and Hamilton's equations. Then the role of network formalism as a unifying conceptual framework for physical systems is emphasized with a review of fundamental papers going back to Kirchhoff's and Maxwell's formulation of Newton's second law. Then the basic notions of bond graph models (ports, junction structures, gyrator) are introduced.
Mathematics Subject Classification ID: 70H99
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 94Cxx
zbMATH DE Number: 536932
zbMATH Keywords: nonresistive systems
zbMATH Keywords: bond graph models
zbMATH Keywords: junction structures
author: B. Maschke
author: Arjan van der Schaft
author: Peter C. Breedveld
reviewed by: Hernan Cendra
MaRDI profile type: Publication
cites work: Q4167627
cites work: Q4174811
cites work: Q3721476
cites work: Q3657476
cites work: Q3785520
cites work: Hamiltonian structures and stability for rigid bodies with flexible attachments
cites work: Q4145201
cites work: Q3338005
cites work: Q3835376
cites work: A bond graph algorithm to determine the equilibrium state of a system
cites work: Q4075409
cites work: Multiport representation of inertia properties of kinematic mechanisms
cites work: Formula manipulation in the bond graph modelling and simulation of large mechanical systems
cites work: Variational analysis of electrical networks
cites work: On the mathematical foundations of electrical circuit theory
cites work: Geometrical formulation of bond graph dynamics with application to mechanisms
cites work: Q5345182
cites work: The local structure of Poisson manifolds
cites work: Q4074052
cites work: Les variétés de Poisson et leurs algèbres de Lie associees
cites work: Lagrange’s Equations for Complex Bond Graph Systems
cites work: Alternative Bond Graph Causal Patterns and Equation Formulations for Dynamic Systems
cites work: Q5812699
cites work: Q3803878
cites work: Q5573210
cites work: Reduction of symplectic manifolds with symmetry
cites work: The mathematical foundations of bond graphs. IV: Matrix representations and causality
cites work: Bond graphs and linear graphs
cites work: Essential gyrators and equivalence rules for 3-port junction structures
full work available at URL: s0016-0032(92)90049-m
OpenAlex ID: W2094571737
description: scientific article; zbMATH DE number 536932