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Complete separability of time-dependent second-order ordinary differential equations (1996)

Cantrijn, F. ; Sarlet, W. ; Vandecasteele, A. ; [et al.]

Springer

Acta applicandae mathematicae 42 (1996), S. 309-334

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ISSN: 1572-9036

Keywords: 34A26 ; 53C05 ; 58Fxx ; separability ; time-dependent second-order equations ; derivations ; forms along a map

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Extending previous work on the geometric characterization of separability in the autonomous case, necessary and sufficient conditions are established for the complete separability of a system of time-dependent second-order ordinary differential equations. In deriving this result, extensive use is made of the theory of derivations of scalar and vector-valued forms along the projection π:J 1 E→E of the first jet bundle of a fibre bundleE → ℝ. Two illustrative examples are discussed, which fully demonstrate all aspects of the constructive nature of the theory.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01064171

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