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The Mathisson equations under the Frenkel-Mathisson supplementary conditionare studied in a Schwarzschild field. The choice of solutions, which describethe motions of the proper center of mass of a spinning test particle, isdiscussed, and the calculation procedure for highly relativistic motions isproposed. The very motions are important for astrophysics while investigatingpossible effects of the gravitational spin-orbit interaction on the particle'sworld line and trajectory.

Mathisson Equations: Non-Oscillatory Solutions in a Schwarzschild Field