COMPARISON BETWEEN FIRST AND SECOND-ORDER GAUSS'S VARIATIONAL EQUATIONS UNDER IMPULSIVE CONTROL

2018 Univelt Inc. All rights reserved. Due to the insufficient 20 page limit, this paper shows, just as an example, how to derive the 2nd-order Gausss variational equation of the inclination under impulsive control. The complete derivation of the 2nd-order Gausss variational equations for all classical and nonsingular orbital elements under impulsive control is done in Ref. [1]. In addition, this paper provides, for an assigned single impulsive velocity variation, the comparison between the orbital elements variations predicted by the 1st-order and 2nd-order with respect to the true Keplerian variations. The gain in accuracy using the 2nd-order over the 1st-order is quantified by numerical Monte Carlo tests. Least-squares estimate of the impulse vector is obtained by inverting the 1st-order and 2nd-order GVEs. The 2nd-order estimation is here proposed for the single-impulse orbital maintenance problem.

COMPARISON BETWEEN FIRST AND SECOND-ORDER GAUSS'S VARIATIONAL EQUATIONS UNDER IMPULSIVE CONTROL Conference Paper