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

abstract

  • © 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 Gauss’s variational equation of the inclination under impulsive control. The complete derivation of the 2nd-order Gauss’s 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.

author list (cited authors)

  • Zhang, G., & Mortari, D.

publication date

  • January 2019