Satellite oscillations in elliptical orbit
Abstract
The planar oscillations of a satellite in an elliptical orbit are described by a system of first order canonical differential equations written in terms of a Hamiltonian function which is analytical in a specified range of eccentricities. With sufficiently small values of the eccentricity this system of equations possesses a single parameter family of hyperbolic solutions which attain equilibrium when the eccentricity is zero. The solution of the equation is found for the case of a coordinate system tied to the satellite center of mass and the effect of the eccentricity on satellite oscillation stability is described mathematically. The conditions for a unique periodic solution of the system are also defined. The purely theoretical analysis adduces neither sample calculations nor applications.
 Publication:

USSR Report Space
 Pub Date:
 February 1985
 Bibcode:
 1985RpSpR....R..47B
 Keywords:

 Elliptical Orbits;
 Orbital Mechanics;
 Oscillations;
 Satellite Orbits;
 Coordinates;
 Differential Equations;
 Hamiltonian Functions;
 Problem Solving;
 Stability;
 Astrodynamics