Inverse problem of mechanics in momentum space

The problem is solved of reproducing a spherically symmetric potential by means of the velocity vector hodograph in a classical mechanics approximation. A definite transcendental equation is obtained for the radial velocity dependence. Considered as an illustration is the problem of the Maxwell fish eye. A relativistic generalization is given. The algorithms constructed can be used to retrieve potentials possessing internal symmetries in the classical or quantum cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 46–50, January, 1985.In conclusion, I am grateful to Prof. Yu. N. Demkov for active and stimulating interest in the research.