Keplerian transition matrices for elliptical orbits.
Abstract
For the case of an elliptical reference orbit, compact analytic formulae are given for the four submatrices composing the state transition matrix (matrizant) of the twobody problem. The transition matrix plays a fundamental role in determining the effects of perturbations on an orbit and in analyzing the stability of an orbit. For example, the submatrix specifying the propagation of velocity perturbations into position perturbations was an essential ingredient in an earlier stability analysis of second species periodic orbits of the restricted three body problem.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 February 1978
 Bibcode:
 1978A&A....63..429H
 Keywords:

 Elliptical Orbits;
 Kepler Laws;
 Matrices (Mathematics);
 Orbit Perturbation;
 Two Body Problem;
 Motion Stability;
 Orbital Mechanics;
 Astronomy;
 TwoBody Problem