A vectorial form for the conic variational equations
Abstract
Variational equations describing deviations from a reference orbit play a central role in space flight analysis. They are widely employed for error estimation in targeting problems, and they have many applications to optimal orbital transfer and spacecraft rendezvous problems. Since the variational equations have so many uses, it is important to have them expressed in a compact form where all terms have a clear physical interpretation to facilitate deployment of the equation. The present investigation is concerned with the derivation of a new vectorial form of the variational equations for conic orbits, taking into account a form in which each term has a definite geometrical interpretation. The result is related to a vectorial form considered by Marec (1969) as well as to the more widely used state transition matrix.
 Publication:

Journal of Guidance Control Dynamics
 Pub Date:
 October 1982
 DOI:
 10.2514/3.19784
 Bibcode:
 1982JGCD....5..537H
 Keywords:

 Astrodynamics;
 Calculus Of Variations;
 Conics;
 Satellite Perturbation;
 Vectors (Mathematics);
 Elliptical Orbits;
 Kepler Laws;
 Orbit Calculation;
 Orbital Elements;
 Space Flight;
 Space Rendezvous;
 Astrodynamics