Analytic partial derivatives for estimating low-thrust parameters.

Abstract

Analytic partial derivatives for estimating orbital low-thrust parameters via differential correction are developed and compared with two different numerical methods. The formulation is independent of the particular thrust model used and is applicable to all physically possible elliptic orbits. The starting point for the development is the set of variational equations of the elliptic orbital elements in the form due to Lagrange. The first time derivatives of the elements are transformed to derivatives with respect to the space variable, true anomaly, and integrated to first order in closed form in a straightforward general perturbations approach, with one exception: particular attention is given to the mean anomaly as influenced by thrust perturbations in the semimajor axis so that the complete first-order effect is included. The partials of the elements are then taken with respect to any given thrust parameter. Two comparisons are made with numerical methods for computing these thrust partials: numerical quotients and numerical integration of the variational equations for thrust.