Regularization of the Lagrange Planetary Equations for Numerical Use

Details Regularization of the Lagrange Planetary Equations for Numerical Use Regularization of the Lagrange Planetary Equations for Numerical Use

Jan 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phdt.......106s&link_type=abstract

Thesis (PH.D.)--THE UNIVERSITY OF TEXAS AT AUSTIN, 1990.Source: Dissertation Abstracts International, Volume: 52-01, Section: B,

Astronomy and Astrophysics

Astronomy

Planetary Equations, Astrodynamics

Scientific paper

The goal of this work is to develop a system of equations which, for a certain dynamic system with a specific range of initial conditions, can be numerically integrated faster and more accurately than the cartesian state vector for the body of interest. It is shown that by using regularization in combination with Lagrange's Planetary Equations, this goal can be accomplished. In this dissertation, the analytic tools needed to regularize Lagrange's Planetary Equations are first developed with the realization that the equations will be numerically integrated. Two dynamical models (the Circular Restricted Three Body Problem and the Oblate Central Body Problem) are then studied for a satellite in an orbit with both high inclination and eccentricity. It is shown that in both dynamical models, the numerical integration of the newly developed equations is both faster and more accurate than integrations of the cartesian state of the satellite. This result is then explained from an analytical viewpoint. The understanding gained through the analytic explanation is then used to refine the equations used to study the motion of the satellite as it experiences solar, lunar and J _2 perturbations. Based on these results, conclusions about the specific system of equations and the numerical integration of systems of equations of this type are drawn. Finally, suggestions for future work are made.

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