Integrals of the equations of motion in the restricted circular threebody problem
Abstract
Analytical expressions for the integral of a conservative system with periodic excitation are obtained along with analytical expressions for the family of integrals of an autonomous conservative system. The integrals are represented as the sum of analytical expressions in powers of a small parameter. An analysis of the integrals demonstrates qualitative differences in the behavior of the solutions near equilibrium in the resonance and nonresonance cases. Integrals are obtained for a system of equations describing perturbed motion near a libration point for the restricted circular threebody problem.
 Publication:

Spacecraft Dynamics and Space Exploration
 Pub Date:
 1986
 Bibcode:
 1986sdse.conf...42S
 Keywords:

 Celestial Mechanics;
 Equations Of Motion;
 Integral Calculus;
 Three Body Problem;
 Harmonic Oscillators;
 Libration;
 Partial Differential Equations;
 Perturbation Theory;
 Resonance;
 Astrodynamics