This paper develops the variational equations associated with a spacecraft trajectory model general enough for most applications of interest. The sensitivity equations of the final state vector with respect to all the independent parameters are derived. The trajectory can have impulsive and/or finite-burn maneuvers, or mass discontinuities. The gradient expressions are derived using the state transition matrix associated with an augmented state vector, which includes the position, velocity, mass, and all other control-related quantities, such as thrust magnitude and direction. This analysis was motivated by the study of abort Moon-Earth trajectories. Examples comparing the performance of these gradients with numerically approximated ones are presented.
展开▼
