Flat coordinates of flat Stäckel systems

In this article we explicitly construct Stäckel separable systems in separation coordinates with the help of separation curve as introduced by Sklyanin. Further, we construct explicit transformation between separable and flat coordinates for flat Stäckel systems. We also exploit the geometric structure of these systems in the obtained flat coordinates. These coordinates generalize the wellknown generalized elliptic and generalized parabolic coordinates introduced by Jacobi.