2017
Том 69
№ 9

All Issues

On the hill stability of motion in the three-body problem

Sosnitskii S. P.

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Abstract

We consider the special case of the three-body problem where the mass of one of the bodies is considerably smaller than the masses of the other two bodies and investigate the relationship between the Lagrange stability of a pair of massive bodies and the Hill stability of the system of three bodies. We prove a theorem on the existence of Hill stable motions in the case considered. We draw an analogy with the restricted three-body problem. The theorem obtained allows one to conclude that there exist Hill stable motions for the elliptic restricted three-body problem.

English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 10, pp 1675-1682.

Citation Example: Sosnitskii S. P. On the hill stability of motion in the three-body problem // Ukr. Mat. Zh. - 2008. - 60, № 10. - pp. 1434–1440.

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