Petr Blaschke
Spherical pedal coordinates
It has been shown that "pedal coordinates" are well suited for describing solutions of force problems in the plane. In particular, central force problems can be solved algebraically in pedal coordinates. Their 3-D analogue seems to be not unique, however. A generalization of pedal coordinates for space curves restricted to the surface of the unit sphere will be presented. We will showcase their usefulness on a number of examples, including: Spherical Kepler problem, movement of a non-planar pendulum, Spherical analogues of Brachistochrone, Catenary and more.
