VECTOR FORMULATIONS FOR SPHERICALLY BOUNDED SEARCH SPACES

In the optimization of spacecraft trajectories, it is often the case that there is some naturally arising bound(s) on the magnitudes of the associated velocities. Such constraints lead to a spherical or, more generally, an elliptical search space. Unfortunately, typical problem transcriptions instead search within a Cartesian box, applying these bounds to each dimension independently. This leads to a search space where nearly half of the search space is known to be useless a priori. The present work investigates an alternate interpretation of a velocity decision vector and assesses the effects of precluding this known sub-optimal space.