On a particular case of motion in the three-body problem - Sosnyts’kyi , S. P. (Ukrains’kyi Matematychnyi Zhurnal, 2026)
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.