Spherical Pedal Coordinates and Calculus of Variations

Planar curves can be described in terms of pedal coordinates. We will introduce a generalization of this notion for curves on a sphere in Euclidean space. It is observed that certain problems in the calculus of variations can be solved with the help of these coordinates [1]. In particular, we show how the notion of spherical pedal coordinates can be used to solve the spherical version of isoperimetric problems and the problem of brachistochrone.