On a particular case of motion in the three-body problem

  • S. P. Sosnyts’kyi Institute of Mathematics of Ukrainian National Academy
Keywords: Symmetrical motion, a Hill stable pair, distal motion, bounded motion

Abstract

UDC 531.36; 531.011

We study the three-body problem in a particular case where two bodies have equal masses, which implies the existence of a manifold of symmetric motions. We are looking for the conditions of existence of bounded (unbounded) symmetric motions.
Our analysis of boundedness (unboundedness) of motions shows that both the structure of the manifold of symmetrical motions and the integrals of energy and angular momentum are essential.

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Published
17.10.2021
How to Cite
Sosnyts’kyi , S. P. “On a Particular Case of Motion in the Three-Body Problem”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 10, Oct. 2021, pp. 1404-13, doi:10.37863/umzh.v73i10.6756.
Section
Research articles