Differential Equation of Sensitivity Matrix for Final Velocity Constraint

In this paper, differential equation of sensitivity matrix of required velocity with respect to position vector is derived for a linearized problem of a spacecraft motion with final velocity constraint. This matrix can be utilized for an implicit guidance of a spacecraft with final position and velocity constraint. The solution is obtained in the presence of aerodynamical force. Therefore, the resulting (equation can be used for trajectory optimization. Moreover, a change of variable is presented to reduce onboard computational burden. In addition, the method is more appropriate for analytical approaches than conventional implicit equations.