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

The Trautman general covariant equations of motion for a test particle interacting with an external field are studied. The relativistic equations of motion are shown to be not resolved in a general case with respect to the acceleration 4-vector, but look like Asub(ik)xDusup(k)/ds=Fi (usup(k) - velocity 4-vector). Formulas are provided to calculate Asub(ik) and Fi using the known Lagrangian functions. Cases of a particle moving in a tensor field of zero, first and second ranks are considered. The Hamilton-Jacobi equation is drawn for an arbitrary interaction law