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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorKress, Jonathan M.
dc.contributor.authorMiller, W., Jr.
dc.contributor.authorPogosyan, G.S.
dc.date.accessioned2008-10-29T03:03:19Z
dc.date.available2008-10-29T03:03:19Z
dc.date.issued2002-07
dc.identifier.citationKalnins, E.G., Kress, J.M., Miller, W., Jr. & Pogosyan, G.S. (2002). Complete sets of invariants for dynamical systems that admit a separation of variables. Journal of Mathematical Physics, 43, 3592.en_US
dc.identifier.issn0022-2488
dc.identifier.urihttps://hdl.handle.net/10289/1189
dc.description.abstractConsider a classical Hamiltonian H in n dimensions consisting of a kinetic energy term plus a potential. If the associated Hamilton–Jacobi equation admits an orthogonal separation of variables, then it is possible to generate algorithmically a canonical basis Q, P where P1 = H, P2, ,Pn are the other second-order constants of the motion associated with the separable coordinates, and {Qi,Qj} = {Pi,Pj} = 0, {Qi,Pj} = ij. The 2n–1 functions Q2, ,Qn,P1, ,Pn form a basis for the invariants. We show how to determine for exactly which spaces and potentials the invariant Qj is a polynomial in the original momenta. We shed light on the general question of exactly when the Hamiltonian admits a constant of the motion that is polynomial in the momenta. For n = 2 we go further and consider all cases where the Hamilton–Jacobi equation admits a second-order constant of the motion, not necessarily associated with orthogonal separable coordinates, or even separable coordinates at all. In each of these cases we construct an additional constant of the motion.en_US
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherAmerican Institute of Physicsen_NZ
dc.relation.urihttp://link.aip.org/link/?JMAPAQ/43/3592/1en_US
dc.rightsCopyright 2002 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jspen_US
dc.subjectMathematicsen_US
dc.subjectclassical mechanicsen_US
dc.titleComplete sets of invariants for dynamical systems that admit a separation of variablesen_US
dc.typeJournal Articleen_US
dc.identifier.doi10.1063/1.1484540en_US
dc.relation.isPartOfJournal of Mathematical Physicsen_NZ
pubs.begin-page3592en_NZ
pubs.editionJulyen_NZ
pubs.elements-id27778
pubs.end-page3609en_NZ
pubs.issue7en_NZ
pubs.volume43en_NZ


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