Transforming St\"{a}ckel Hamiltonians of Benenti type to polynomial form
Exactly Solvable and Integrable Systems
2021-01-05 v1 Mathematical Physics
math.MP
Abstract
In this paper we discuss two canonical transformations that turn St\"{a}ckel separable Hamiltonians of Benenti type into polynomial form: transformation to Vi\`ete coordinates and transformation to Newton coordinates. Transformation to Newton coordinates has been applied to these systems only very recently and in this paper we present a new proof that this transformation indeed leads to polynomial form of St\"{a}ckel Hamiltonians of Benenti type. Moreover we present all geometric ingredients of these Hamiltonians in both Vi\`ete and Newton coordinates.
Keywords
Cite
@article{arxiv.2101.00444,
title = {Transforming St\"{a}ckel Hamiltonians of Benenti type to polynomial form},
author = {Jean de Dieu Maniraguha and Krzysztof Marciniak and Célestin Kurujyibwami},
journal= {arXiv preprint arXiv:2101.00444},
year = {2021}
}