Researches on the Restricted ThreeBody Problem. II: Periodic Solutions and Arcs for u=0
Abstract
This work considers periodic solutions and arcsolutions (solutions with consecutive collisions) of the plane circular restricted problem of three bodies for μ=0. To study the mutual arrangement of these solutions in phase space, we introduce a global section Γ of the phase space. Each solution is represented in Γ by some points (at least one), and families of solutions are represented by curves (the characteristics). We give a concrete description of the arrangement of the characteristics in the threedimensional space Γ. The solutions studied here play a fundamental role in generating periodic solutions of the restricted problem for small μ≠0.
 Publication:

Celestial Mechanics
 Pub Date:
 July 1978
 DOI:
 10.1007/BF01233089
 Bibcode:
 1978CeMec..18....9B
 Keywords:

 Celestial Mechanics;
 Orbital Mechanics;
 Three Body Problem;
 Collisions;
 Curves (Geometry);
 Hamiltonian Functions;
 Hyperspaces;
 Orbital Elements;
 Periodic Functions;
 Two Body Problem;
 Astronomy