Other
Scientific paper
Jan 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998phyd..112..310m&link_type=abstract
Physica D: Nonlinear Phenomena, Volume 112, Issue 1-2, p. 310-318.
Other
2
Periodic Solutions, Restricted Three-Body Problem, Reduction, Smleic Caling
Scientific paper
We use the methods of symplectic scaling and reduction to show that the reduced spatial three-body problem with one small mass is to the first approximation the product of the spatial restricted three-body problem and a harmonic oscillator. This allows us to prove that a nondegenerate periodic solution of the spatial restricted three-body problem can be continued into the reduced three-body problem with one small mass. The spatial three-body problem and the spatial restricted three-body problem admit two time-reversing symmetries. A solution which hits the fixed set of one of the symmetries at time 0 and the fixed set of the other at time T will be periodic of period 4T and its orbit will be symmetric with respect to both symmetries. Such solutions are called doubly symmetric. We prove that a nondegenerate doubly symmetric periodic solution of the spatial restricted three- body problem can be continued into the reduced three-body problem with one small mass.
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