Superintegrable St\"ackel Systems on the Plane: Elliptic and Parabolic Coordinates
Andrey V. Tsiganov
TL;DR
This paper explores the construction of additional integrals of motion for Stäckel systems on the plane, focusing on elliptic and parabolic coordinates, using addition theorems applied to angle variables.
Contribution
It provides explicit examples of integrals of motion for elliptic and parabolic coordinate systems, expanding the understanding of superintegrability in these systems.
Findings
Explicit examples of integrals of motion for elliptic coordinates
Explicit examples of integrals of motion for parabolic coordinates
Demonstration of the application of addition theorems to angle variables
Abstract
Recently we proposed a generic construction of the additional integrals of motion for the St\"ackel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle variables for elliptic and parabolic coordinate systems on the plane.
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