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Newton systems of cofactor type in Euclidean and Riemannian spaces
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
2001 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

We study second order ordinary differential equations of Newton type with integrals of motion that depend quadratically on the velocity. In particular, we introduce the class of cofactor pair systems, which admit two quadratic integrals of motion of a special form. It is shown that this implies that the system in fact admits a full set of Poisson commuting integrals of motion, and consequently is completely integrable. Methods are given for testing whether a given Newton system belongs to this class, and for constructing infinite families of cofactor pair systems. Several known result about separable potentials are included in the theory as special cases. As an application, it is shown how to extend the classical concept of Stäckel separability to a class of time-dependent potentials.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2001. , p. 97
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 719
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-143521ISBN: 917373120X (print)OAI: oai:DiVA.org:liu-143521DiVA: diva2:1164631
Public defence
2001-11-09, C3, hus C, Campus Valla, Linköping, 13:15 (English)
Opponent
Available from: 2017-12-11 Created: 2017-12-11 Last updated: 2018-01-22Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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  • Other style
More styles
Language
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  • nn-NB
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  • Other locale
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Output format
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