Equations of motion for a test particle in an external field in the special theory of relativity

A study is made of the general-covariant equations of motion of Trautman for a particle interacting with an external field. It is shown that in the general case the relativistic equations of motion are not solvable for the acceleration four-vector but have the form a_ik(Du^kds) = F_i. Formulas are given fora _ik and F_i by means of which they can be calculated in terms of the known Lagrangian. Examples are given of the motion of a particle in tensor fields of rank zero, one, and two. The Hamilton-Jacobi equation for an arbitrary interaction law is constructed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 43–48, March, 1977.The author wishes to thank Professor V. I. Rodichev for a useful discussion on the work.