Generalized submersiveness of second-order ordinary differential equations

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June 2009, 1(2): 209-221. doi: 10.3934/jgm.2009.1.209

Generalized submersiveness of second-order ordinary differential equations

W. Sarlet ^1, , G. E. Prince ^2, and M. Crampin ^1,

1.	Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281, 9000 Ghent, Belgium, Belgium
2.	Department of Mathematics and Statistics, La Trobe University, Melbourne, Victoria 3086, Australia

Received March 2009 Revised June 2009 Published July 2009

Abstract
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We generalize the notion of submersive second-order differential equations by relaxing the condition that the decoupling stems from the tangent lift of a basic distribution. It is shown that this leads to adapted coordinates in which a number of first-order equations decouple from the remaining second-order ones.

Keywords: integrable distributions, decoupling., Second-order differential equations, tangent bundle geometry.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.

Citation: W. Sarlet, G. E. Prince, M. Crampin. Generalized submersiveness of second-order ordinary differential equations. Journal of Geometric Mechanics, 2009, 1 (2) : 209-221. doi: 10.3934/jgm.2009.1.209

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