Stationary Solutions in Simplified Resonance Cases of the Restricted ThreeBody Problem
Abstract
In the planar elliptic problem SunJupitermassless body we consider the resonances of mean motion 3/2, 2/1, 3/1, 7/3 and 1/3. Shortperiod effects are eliminated by Schubart's averaging method. Applying a minimization technique, stationary solutions can be found in the given resonance cases. Some of these solutions are wellknown as periodic solutions in the rigorous (i.e., unaveraged) restricted problem. It is illustrated how one can construct in a numerical way a linearized theory of motion around a stationary solution and results are presented.
 Publication:

Celestial Mechanics
 Pub Date:
 February 1980
 DOI:
 10.1007/BF01230892
 Bibcode:
 1980CeMec..21..157B
 Keywords:

 Asteroids;
 Jupiter (Planet);
 Resonance;
 Solar System;
 Three Body Problem;
 Astrodynamics;
 Motion Stability;
 Orbital Mechanics;
 Periodic Functions;
 Astronomy