Flat coordinates for flat St\"ackel systems
Krzysztof Marciniak, Maciej Blaszak
TL;DR
This paper explicitly constructs transformations between separable and flat coordinates for flat Stäckel systems, revealing their structure and connecting to known elliptical coordinates in the elliptic case.
Contribution
It provides explicit formulas for coordinate transformations in flat Stäckel systems, enhancing understanding of their geometric structure and relation to classical elliptical coordinates.
Findings
Explicit transformation formulas between separable and flat coordinates.
Identification of these coordinates with generalized elliptical coordinates.
Deeper insight into the structure of flat Stäckel systems.
Abstract
In this article we explicitely construct transformation bewteen separable and flat coordinates for flat St\"ackel systems and exploit the structre of these systems in flat coordinates. In the elliptic case these coordinates become well known generalized elliptical coordinates of Jacobi.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Advanced Topics in Algebra · Nonlinear Waves and Solitons