Lie point symmetries and first integrals: the Kowalevsky top
arXiv:nlin/0201023 · doi:10.1063/1.1561157
Abstract
We show how the Lie group analysis method can be used in order to obtain first integrals of any system of ordinary differential equations. The method of reduction/increase of order developed by Nucci (J. Math. Phys. 37, 1772-1775 (1996)) is essential. Noether's theorem is neither necessary nor considered. The most striking example we present is the relationship between Lie group analysis and the famous first integral of the Kowalevski top.
23 pages
References in corpus (2)
Cited by in corpus (6)
- Lorenz integrable system moves à la Poinsot
- A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
- Are all classical superintegrable systems in two-dimensional space linearizable?
- Superintegrable systems in non-Euclidean plane: hidden symmetries leading to linearity
- On the Reduction Process of Nucci-Reduce Algorithm for Computing Nonlocal Symmetries of Dynamical Systems:A case study of the Kepler and Kepler-related problems
- Two Flows Kowalevski Top as the Full Genus Two Jacobi's Inversion Problem and Sp(4,) Lie Group Structure