Geodesic
Stability of the motion of rotating test bodies in the relativistic theory of gravitation
Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 2, pp. 285-296

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The stability of circular, noncircular, and infinite motions of rotating test bodies in the field of a static spherically symmetric body is investigated in the framework of Logunov's relativistic theory of gravitation on the basis of Papapetrou's equations. Lyapunov's first method is used to find the regions of instability of circular motions; to find the stability regions appropriate Lyapunov functions are found from the integrals of the motion. It is shown that the noncircular and infinite motions are Lyapunov unstable; conditions are found under which these motions are stable over a finite time interval. The results are compared with the conclusions drawn about the stability of the motion of rotating bodies in the general theory of relativity. 
@article{TMF_1988_77_2_a12,
     author = {A. A. Bakhan'kov},
     title = {Stability of the motion of rotating test bodies in the relativistic theory of gravitation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {285--296},
     publisher = {mathdoc},
     volume = {77},
     number = {2},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_77_2_a12/}
}
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A. A. Bakhan'kov. Stability of the motion of rotating test bodies in the relativistic theory of gravitation. Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 2, pp. 285-296. http://geodesic.mathdoc.fr/item/TMF_1988_77_2_a12/