Soviet Physics Journal

, Volume 20, Issue 3, pp 312–316 | Cite as

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

  • N. N. Razgovorov


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 aik(Dukds) = Fi. Formulas are given foraik and Fi 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.


Relativistic Equation External Field Test Particle Special Theory Tensor Field 
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Literature cited

  1. 1.
    A. Trautman, Bull. Acad. Polon. Sci., cl. III,5, 721 (1957).Google Scholar
  2. 2.
    E. Schmutzer, Symmetry and Laws of Conservation in Physics [Russian translation], Mir, Moscow (1974), p. 62.Google Scholar
  3. 3.
    V. I. Rodichev, The Theory of Gravitation in an Orthogonal Frame of Reference [in Russian], Nauka, Moscow (1974), p. 40; see also: Einstein Collection [in Russian], Nauka, Moscow (1968), p. 166.Google Scholar
  4. 4.
    N. N. Razgovorov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 3, 143 (1976).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • N. N. Razgovorov
    • 1
  1. 1.All-Union Correspondence Institute of Machine ConstructionUSSR

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