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- Title
Reduction and Reconstruction Aspects of Second-Order Dynamical Systems with Symmetry.
- Authors
Crampin, M.; Mestdag, T.
- 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.
- Subjects
SYSTEM analysis; NUMERICAL solutions to differential equations; VECTOR analysis; SYMMETRIC spaces; GEOMETRIC connections; LIE groups; RECONSTRUCTION (Graph theory); ANALYTICAL mechanics
- Publication
Acta Applicandae Mathematicae, 2009, Vol 105, Issue 3, p241
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-008-9274-7