Time-discretization of Hamiltonian dynamical systems
type: Item
instance of: scholarly article
title: Time-discretization of Hamiltonian dynamical systems
zbMATH Open document ID: 0810.65069
DOI: 10.1016/0898-1221(94)00189-8
author: Y. Shibberu
publication date: 1995-04-09T00:00:00Z
full work available at URL: https://scholar.rose-hulman.edu/cgi/viewcontent.cgi
review text: Difference equations for Hamiltonian systems are derived from a discrete variational principle (DTH -- discrete time Hamiltonian). This article is focused on the basic ideas of DTH dynamics for the case of autonomous systems with one degree of freedom. Variational principles of mechanical systems are recalled in section 2. Section 3 introduces notation for describing piecewise-linear, continuous functions. In the next section the DTH principle of stationary action is discussed and applied to DTH dynamics. Simulation results for two Newtonian potential systems are presented in section 6, and section 7 presents, without proofs, some extensions to nonautonomous systems with \(n\)-degrees of freedom.
reviewed by: Yves Cherruault
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 699056
zbMATH Keywords: Hamiltonian dynamical systems
zbMATH Keywords: difference equations
zbMATH Keywords: discrete variational principle
zbMATH Keywords: discrete time Hamiltonian
zbMATH Keywords: autonomous systems
zbMATH Keywords: nonautonomous systems
MaRDI profile type: Publication
OpenAlex ID: W2049014179
cites work: Q5683729
cites work: Discrete numerical methods in physics and engineering
cites work: DISCRETE HAMILTONIAN MECHANICS
cites work: The discrete variational approach to the Euler-Lagrange equation
cites work: Q3953228
cites work: Q5512814
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 699056