Analytic solutions for intermediate-thrust arcs of rocket trajectories in a Newtonian field
Mayer's variational problem of determining the optimum trajectories of a rocket moving with constant exhaust velocity and bounded mass flow rate in a Newtonian field is considered. New analytic solutions are obtained for plane intermediate-thrust arcs, using the canonical system of equations of the variational problem and the properties of the switching function. These solutions represent certain spiral trajectories. In motion with a fixed time, at arbitrary angular distances, these solutions satisfy Robbins' necessary optimum condition. As an example, the problem of minimizing the characteristic velocity of flight between elliptic orbits is considered.
scientific article; zbMATH DE number 1080158