Linear guidance laws for space missions

A general analysis of guidance laws is presented along with a review of the propagation of state perturbations. Linearized guidance laws are derived for fixed and variable time of arrival, and for the Shuttle phasing and height guidance maneuvers. In general, six interrelated partials are involved in each guidance law. These partials relate the maneuver delta velocity and the time of flight to perturbations in initial position, velocity, and time. The partials can be expressed as a function of a single fundamental guidance partial, which relates the maneuver to the final position perturbation, and the partials from the upper row of the augmented time transition matrix (augmented with the dynamical state vector). Guidance can be interpreted as a form of offset targeting.