The Lyapunov stability of circular motions of spinning test bodies in the Schwarzschild field has been considered. For Papapetrou cquations the generalized supplementary conditions Soiu, = kSiiui, k = const, i , j = 1, 2, 3, have been chosen. Four of the first integrals of motion have been indicated. With the aid of Lyapunov functions the domains of stable motions have been found.
Der EinfluQ der Zusatzbedingungen fur die Papapetrou-Gleichungen auf die Ljapunovsche Stabilitlt der BewegungInhnltsubersicht. In der vorliegenden Arbeit wird die Ljapunovsche Stabilitat der Kreisbeu-egung eines rotierenden Testteilchens im Schwarzschild-Feld untersucht. Dabei werden die folgendcn Zusiltzbedingungeri fur die Papapetrou-Gleichungen angenommen: Soiuo = kSESiiui, wobei k = const und i , j = 1, 2 , 3 sind. Es werden die vier ersten Bewegungsintegrale angegeben. Mit Hilfe von Ljnpnnov-Eunktionen werden die Bereiche der stabilen Bewegung gefunden.
DSDS DS + U"U, ---O J DS"B where DJDs denotes absolute derivative, rn = rnoc2, rno is the rest mass of the body, u" == dx:"Jdsits velocity, R$PY is the curvature tensor of Riemann space-time, where the body moves.While deriving equations (I) one did not specify the choice of the world line, which represents test body motion. Due to this, the system (1) is not complete : there are only three independent equations for determination of six spin tensor components. In order
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