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Geometric characterization of separable second-order differential equations

Published online by Cambridge University Press:  24 October 2008

Eduardo Martínez ,
José F. Cariñena  and
Willy Sarlet
Eduardo Martínez
Affiliation:
Departamento de Física Teórica, Universidad de Zaragoza, E-50009 Zaragoza, Spain
José F. Cariñena
Affiliation:
Departamento de Física Teórica, Universidad de Zaragoza, E-50009 Zaragoza, Spain
Willy Sarlet
Affiliation:
Instituut voor Theoretische Mechanica, Universiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium
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Abstract

We establish necessary and sufficient conditions for the separability of a system of second-order differential equations into independent one-dimensional second-order equations. The characterization of this property is given in terms of geometrical objects which are directly related to the system and relatively easy to compute. The proof of the main theorem is constructive and thus yields a practical procedure for constructing coordinates in which the system decouples.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 1 , January 1993 , pp. 205 - 224
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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