The restricted planar isosceles three-body problem with non-negative energy |
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| Authors: | Josep Maria Cors César Castilho Claudio Vidal |
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| Institution: | (1) Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Barcelona, Spain;(2) Departamento de Matemática, Universidade Federal de Pernambuco, Recife, Brazil;(3) Departamento de Matemática, Universidad del Bío Bío, Concepción, Chile |
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| 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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| Keywords: | 3-Body problem Restricted isosceles problem Global flow Sitnikov-type restricted problem |
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