Construction of autonomous canonical systems when the Hamiltonian depends explicitly on time
type: Item
instance of: scholarly article
title: Construction of autonomous canonical systems when the Hamiltonian depends explicitly on time
zbMATH Open document ID: 0638.70011
DOI: 10.1016/0020-7225(88)90057-2
author: Dominic G. B. Edelen
published in: International Journal of Engineering Science
publication date: 1988-01-01T00:00:00Z
review text: If the Hamiltonian function of a dynamical system depends explicitly on the time variable, the resulting system of Hamilton's equations is not autonomous. An explicit method of extension is given whereby a new pair of conjugate variables is introduced so that the extended system remains Hamiltonian, but becomes autonomous. The new generalized coordinate turns out to be the instantaneous value of the original Hamiltonian function of the dynamical orbit, while the new conjugate momentum is the old time variable. A fully canonical formalism is obtained, together with a redefined Poisson bracket, a Poisson algebra of smooth functions on the extended phase space, and a Hamilton-Jacobi theory.
Mathematics Subject Classification ID: 70H15
Mathematics Subject Classification ID: 70H20
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 4041358
zbMATH Keywords: Hamiltonian function
zbMATH Keywords: generalized coordinate
zbMATH Keywords: dynamical orbit
zbMATH Keywords: conjugate momentum
zbMATH Keywords: Poisson bracket
zbMATH Keywords: Poisson algebra of smooth functions
zbMATH Keywords: extended phase space
zbMATH Keywords: Hamilton-Jacobi theory
MaRDI profile type: Publication
full work available at URL: 0020-7225(88)90057-2
OpenAlex ID: W2029679925
cites work: Q5816742
cites work: Q4167662
cites work: Q5729749
cites work: Q5541903
cites work: Q5515668
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description: scientific article; zbMATH DE number 4041358