On the determination of the potential function from given orbits
The paper deals with the problem of finding the field of force that generates a given ()-parametric family of orbits for a mechanical system with degrees of freedom. This problem is usually referred to as the inverse problem of dynamics. We study this problem in relation to the problems of celestial mechanics. We state and solve a generalization of the Dainelli and Joukovski problem and propose a new approach to solve the inverse Suslov’s problem. We apply the obtained results to generalize the...