Rocket trajectory optimization - 1950-1963

Early Years I FIRST became interested in the possibility of space travel when, as a child, I read H. G. Wells' novel First Men on the Moon. Later, I was presented one Christmas with a copy of Jules Verne's novel From Earth to Moon and a Trip Around It, but it was not until I came across the book Rockets Through Space by P. E. Cleator, when browsing in a Birmingham library, that I realized that journeys to other worlds need not remain at the level of fantasy. Phil Cleator founded the British Interplanetary Society (BIS) in 1933 and in his book described some experimental firings of liquid-fuel rockets carried out under the auspices of this organization; he speculated that this type of vehicle could be used to explore the solar system. As a young student, I was fascinated by the vistas opened up and immediately joined the society, being rewarded with a set of drawings and commentary describing a solid-fuel rocket thought capable of placing a small party of members on the moon. Unfortunately (or, possibly, fortunately), no sponsor prepared to foot the bill for building this device had stepped forward before the war was declared and the society went into hibernation as I, together with many of its members, joined the armed services. On being released from the army in 1946, I returned to Cambridge University to complete a mathematics degree course and was there contacted ^y Len Carter who, as secretary, had beeri instrumental in amalgamating various rocket groups in the United Kingdom into a reformed BIS. i rejoined the society and began to take an interest in the research work it was encouragiiig. The calculation of interplanetary rocket trajectories was clearly the problem for which my mathematical training best fitted me to make a contribution. I soon discovered that very little work had been done in this area. 1) The equation of motion of a rocket, namely, so that for a short burst of motor activity (t0, ^), we have