English

Reduction and reconstruction aspects of second-order dynamical systems with symmetry

Differential Geometry 2009-02-16 v1 Mathematical Physics math.MP

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

Cite

@article{arxiv.0807.0156,
  title  = {Reduction and reconstruction aspects of second-order dynamical systems with symmetry},
  author = {M. Crampin and T. Mestdag},
  journal= {arXiv preprint arXiv:0807.0156},
  year   = {2009}
}

Comments

28 pages, to appear in Acta Appl. Math

R2 v1 2026-06-21T10:56:25.523Z