Properties of linearized mappings associated with periodic orbits in the three-body problem |
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| Authors: | P C Kammeyer |
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| Institution: | 1. Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Texas, USA
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| Abstract: | In this paper three results on the linearized mapping associated with the plane three body problem near a periodic orbit are established. It is first shown that linear stability of such an orbit is independent of initial position on the orbit and of coordinate system. Second, the relation of Hénon connecting the rates of change of rotation angle and period on an isoenergetic family of periodic orbits is proved, together with a similar relation for families of orbits closing exactly in a rotating coordinate system. Finally, a condition for a critical orbit is given which is applicable to any family of periodic orbits. |
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