THE TREATMENT OF THE EARTH OBLATENESS EFFECT IN TRAJECTORY OPTIMIZATION IN EQUINOCTIAL COORDINATES

The effect of the first order secular perturbation due to the zonal ha rmonic J(2) in optimal transfer problems is analyzed. The J(2)-induced acceleration is transformed from the polar frame to the direct equino ctial frame and the dynamic system for the thrust and oblateness pertu rbations formed. The differential equations for the adjoints are then derived in analytic form such that the full six-state optimal transfer system is integrated numerically. Furthermore, the complete averaged system is also presented with the averaged state and adjoint rates due to the thrust perturbation obtained by numerical quadrature, and the ones due to the oblateness effect derived analytically. (C) 1997 Elsev ier Science Ltd.