A method of numerical integration and solution of variational equations for perturbed twobody motion
Abstract
The numerical integration of the differential equations of perturbed twobody motion and their variational equations is modified to improve the accuracy of computation of the solution and its partial derivatives. The equations of motion are transformed to a new set of differential equations by two different techniques. One is the Sundman transformation of the time which converts time from the independent variable to an additional dependent variable and defines a new independent variable. The other is energy stabilization which introduces negative energy explicitly into the equations of motion as an additional dependent variable. The transformed equations of motion are placed in a generalized canonical form for which the Hamiltonian is a constant of the motion. It is shown that the solution of the transformed equations is a valid solution of the perturbed twobody problem if and only if the Hamiltonian of the transformed equations equals the gravitational constant.
 Publication:

Ph.D. Thesis
 Pub Date:
 April 1977
 Bibcode:
 1977PhDT........66G
 Keywords:

 Differential Equations;
 Numerical Integration;
 Two Body Problem;
 Variational Principles;
 Celestial Mechanics;
 Equations Of Motion;
 Hamiltonian Functions;
 Perturbation Theory;
 Scalars;
 Astrodynamics