Calculation of singular extremal rocket trajectories

The equations determining singular intermediate-thrust extremal arcs in an inverse square law gravitational field, for which a rocket's propellant expenditure is stationary with respect to small variations, are transformed into a form more convenient for numerical computation in the general three-dimensipnal case. It is shown that the set of essentially distinguishable arcs is doubly infinite and the types of behavior of the rocket thrust along these trajectories are described. A comparison is made between various orbital transfers effected via these arcs and optimal two-impulse transfers.