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Reduction and Reconstruction Aspects of Second-Order Dynamical Systems with Symmetry |
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| Authors: | M. Crampin T. Mestdag |
| Affiliation: | (1) Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281, 9000 Ghent, Belgium;(2) Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA |
| Abstract: | We examine the reduction process of a system of second-order ordinary differential equations which is invariant under a Lie group action. With the aid of connection theory, we explain why the associated vector field decomposes in three parts and we show how the integral curves of the original system can be reconstructed from the reduced dynamics. An illustrative example confirms the results. |
| Keywords: | Second-order dynamical system Symmetry Principal connection Reduction Reconstruction |
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