Resonance in the restricted problem of three bodies with shortperiod perturbations in the elliptic case.
Abstract
The motion of an asteroid of negligible mass moving in the gravitational field of Jupiter is considered as part of an elliptical system with the sun at one focus, and defined by the expanded powers of a small parameter epsilon, which represents the ratio of Jupiter's mass compared with that of the sun. Hamiltonian equations of motion are presented for the asteroid, whereby the osculating elements are obtained until epsilon vanishes. The Von Zeipel method is employed to achieve the elimination of the shortperiodic terms.
 Publication:

IAU Colloq. 41: Dynamics of Planets and Satellites and Theories of their Motion
 Pub Date:
 1978
 DOI:
 10.1007/9789400998094_40
 Bibcode:
 1978ASSL...72..339B
 Keywords:

 Asteroids;
 Elliptical Orbits;
 Jupiter (Planet);
 Orbit Perturbation;
 Solar Orbits;
 Three Body Problem;
 Orbit Calculation;
 Orbital Elements;
 Planetary Gravitation;
 Resonance;
 Astronomy;
 Resonances:ThreeBody Problem