Abstract
We consider a restricted three-body problem consisting of two positive equal masses m 1 = m 2 moving, under the mutual gravitational attraction, in a collision orbit and a third infinitesimal mass m 3 moving in the plane P perpendicular to the line joining m 1 and m 2. The plane P is assumed to pass through the center of mass of m 1 and m 2. Since the motion of m 1 and m 2 is not affected by m 3, from the symmetry of the configuration it is clear that m 3 remains in the plane P and the three masses are at the vertices of an isosceles triangle for all time. The restricted planar isosceles three-body problem describes the motion of m 3 when its angular momentum is different from zero and the motion of m 1 and m 2 is not periodic. Our main result is the characterization of the global flow of this problem.
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Cors, J.M., Castilho, C. & Vidal, C. The restricted planar isosceles three-body problem with non-negative energy. Celest Mech Dyn Astr 103, 163–177 (2009). https://doi.org/10.1007/s10569-008-9178-x
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DOI: https://doi.org/10.1007/s10569-008-9178-x