Symplectic schemes for nonautonomous Hamiltonian system
type: Item
instance of: scholarly article
title: Symplectic schemes for nonautonomous Hamiltonian system
zbMATH Open document ID: 0922.58030
DOI: 10.1007/BF02011893
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 1999-10-11T00:00:00Z
review text: The construction of symplectic schemes for autonomous Hamiltonian system has been systematically studied. The author considers the following system of canonical equations \[ {dp_i\over dt}= -{\partial H\over\partial q_i},\quad {dq_i\over dt}= {\partial H\over\partial p_i},\quad i=1,2,\dots,n \] with Hamiltonian function \(H(p_1,\dots, p_n, q_1,\dots, q_n,t)\). Using the time \(t\) as an additional dependent variable, the author considers the extended \(2n+2\) dimensional phase space \(z= (p_1,\dots, p_n,h\), \(q_1,\dots, q_n,t)\), here \(t\) and \(h\) being merely alternative notations for \(q_{n+1}\) and \(p_{n+1}\). Note that after adding the time \(t\) to the mechanical variables, every system becomes conservative. The author generalizes the method of constructing symplectic schemes by generating function in the case of autonomous Hamiltonian system to that of nonautonomous system, using the scheme mentioned above.
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 1281427
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: symplectic schemes
zbMATH Keywords: nonautonomous system
zbMATH Keywords: generating function
author: Qin Meng Zhao
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Q4174811
cites work: Q3729973
cites work: Q3780530
cites work: Symplectic integration of Hamiltonian systems
description: scientific article; zbMATH DE number 1281427