A Comparative Study of the Calculation of Partial Derivatives in Space Dynamics

Abstract

In the rigorous treatment of the partial derivatives of the instantaneous state vector of a spacecraft with respect to the initial state vector the pertinent variational equations are usually integrated numerically. Since the procedure is a laborious one, its optimization is desirable. It is to be expected that a broader knowledge of the mathematical aspects of the variational equations is remunerated by an improved computational efficiency.

The means for making the integration of the equations faster and more accurate in applications to orbit determination and error analysis are elaborated and compared in relation to the choice of coordinates and independent variables, and the types of spacecraft orbits. Starting with the classical form of the variational equations and the utilization of regularized coordin-Baker method of solving a system of linear differential equation and the utilization of regularized coordinates for the calculus of partial derivatives are investigated. Several case studies lead to distinctive results in terms of time consumption and accuracy.