Keplerian transition matrices for elliptical orbits

Details Keplerian transition matrices for elliptical orbits Keplerian transition matrices for elliptical orbits

Feb 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978a%26a....63..429h&link_type=abstract

Astronomy and Astrophysics, vol. 63, no. 3, Feb. 1978, p. 429-432.

Mathematics

1

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

Scientific paper

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 two-body 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.

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