On reciprocal equivalence of St\"ackel systems
Abstract
In this paper we ivestigate St\"ackel transforms between different classes of parameter-dependent St\"ackel separable systems of the same dimension. We show that the set of all St\"ackel systems of the same dimension splits to equivalence classes so that all members within the same class can be connected by a single St\"ackel transform. We also give an explicit formula relating solutions of two St\"ackel-related systems. These results show in particular that any two geodesic St\"ackel systems are St\"ackel equivalent in the sense that it is possible to transform one into another by a single St\"ackel transform. We also simplify proofs of some known statements about multiparameter St\"ackel transform.
Keywords
Cite
@article{arxiv.1201.0446,
title = {On reciprocal equivalence of St\"ackel systems},
author = {Maciej Blaszak and Krzysztof Marciniak},
journal= {arXiv preprint arXiv:1201.0446},
year = {2018}
}
Comments
We clarified arguments in Section 3, Studies in Applied Mathematics 2012