A semianalytic theory for satellite orbit prediction
Abstract
A semianalytical theory for satellite orbit prediction was developed. The conservative perturbation affecting the satellite is handled analytically using the LieHori approach, and a numerical version of the method of averaging is used to average the nonconservative perturbation over one revolution of the satellite. The generalized LieHori method and the averaging method are compared. In the comparison the equivalence of the two methods to the second order in the small parameter is shown. However, the approach used can be extended to demonstrate the equivalence for higher orders. To illustrate the equivalance, Duffing's equation, the van der Pol equation, the oscillator with quadratic damping problem, and the oscillator with linear damping problem are solved using each method. The equivalence is used to develop a semianalytical theory for satellite orbit prediction. The mean element rates are numerically integrated, and the osculating elements are recovered by transforming to the osculating element space. The semianalytical method developed is compared with numerical integration.
 Publication:

Ph.D. Thesis
 Pub Date:
 1985
 Bibcode:
 1985PhDT........28A
 Keywords:

 Equations Of Motion;
 Nonlinear Equations;
 Orbital Position Estimation;
 Satellite Orbits;
 Double Cusps;
 Duffing Differential Equation;
 Lie Groups;
 Mathematical Logic;
 Numerical Analysis;
 Orbit Calculation;
 Astrodynamics