On a Special Case of Motion in the Three-Body Problem

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