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.

References in corpus (4)

• On maximally superintegrable systems
• On algebraic construction of certain integrable and super-integrable systems
• Leonard Euler: addition theorems and superintegrable systems
• Structure Theory for Extended Kepler-Coulomb 3D Classical Superintegrable Systems

Cited by in corpus (3)

• On superintegrable systems separable in Cartesian coordinates
• Elliptic curve arithmetic and superintegrable systems
• Transformation of the Stackel matrices preserving superintegrability