Superintegrable Stäckel Systems on the Plane: Elliptic and Parabolic Coordinates

Abstract

Recently we proposed a generic construction of the additional integrals of motion for the Stäckel 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.

Keywords

• bility
• superintegrability
• separation of variables
• Abel equations
• addition theorems