Determination of separation coordinates for potential and quasi-potential Newton systems
2003 (English)Doctoral thesis, comprehensive summary (Other academic)
When solving Newton systems q = M(q), q ϵ Rn, by the method of separation of variables, one has to determine coordinates in which the related Hamilton-Jacobi equation separates.
The problem of finding separation coordinates for potential Newton systems q = -∇V (q) goes back ta Jacobi. In the first part of this thesis we give a complete solution to this classical problem. It can also be used to find separation coordinates for the Schrödinger equation.
In the second part of this thesis, we study separability for quasi-potential systems q = -A(q)-1∇W(q) of generic cofactor pair type. We define separation coordinates that give these systems separable Stäckel form. The two most important families of these coordinates (cofactor-elliptic and cofactor-parabolic) generalize the Jacobi elliptic coordinates, and are shown to be defines by elegant rational equations.
Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2003. , 18 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 845
IdentifiersURN: urn:nbn:se:liu:diva-23168Local ID: 2573ISBN: 91-7373-755-0OAI: oai:DiVA.org:liu-23168DiVA: diva2:243482
2003-11-07, Sal C3, Hus C, Linköpings Universitet, Linköping, 10:15 (Swedish)
Benenti, Sergio, Professor
List of papers