# American Institute of Mathematical Sciences

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

## Generalized submersiveness of second-order ordinary differential equations

 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

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.
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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