An ideal reference frame for perturbed orbital motion
Abstract
An ideal reference frame has been developed for computing perturbed orbital motion for the twobody problem. This ideal frame can serve as the basis for future onorbit optimization, guidance and navigation development. The dependent and independent variables of the dynamical problem are transformed into a unit vector in a relative frame and a new independent variable, an arbitrary reference angle. For the unperturbed problem (motion subject to only the inversesquare force of gravitational attraction), the differential equations describing the transformed and also redundant system of variables reduce to a vector and scalar harmonic oscillator, and a form of Kepler's equation. These equations are readily integrated; the solution is expressed in terms of a set of 'natural' constants or elements. The formulation expressed by these equations is stable, singularity free, and regular. For general perturbations (forces that are 'small' when compared to the analytically removed inversesquare force), only the perturbed differential equations are integrated. These equations are relatively simple and physically meaningful.
 Publication:

Astrodynamics 1987
 Pub Date:
 1988
 Bibcode:
 1988asdy.conf...62J
 Keywords:

 Astrodynamics;
 Orbit Perturbation;
 Reference Systems;
 Two Body Problem;
 Kepler Laws;
 Variational Principles;
 Astrodynamics