TABLE OF CONTENTS The problem of minimum-fuel time-fixed orbit transfer and rendezvous using continuous low thrust bounded from above and below is analyzed next. Specific impulse, or I sp, is no longer considered to be a fixed quantity during the transfer and is now allowed to vary between well-defined minimum and maximum bounds such that both thrust magnitude and direction are optimized to yield the overall minimum-fuel solution. For example, for the case of the electric engine, we can assume that the power remains constant such that the thrust magnitude is inversely proportional to the specific impulse, which is continuously adjusted by varying the beam voltage. We first revisit the fundamentals of flight mechanics and low-thrust propulsion developed in Refs. [12], [17], and [18] and derive the equivalent expressions for the optimal controls for the thrust-magnitude unconstrained case using equinoctial elements instead of the usual Cartesian coordinates. The necessary conditions for optimality for the thrust-bounded case are derived following Refs. [11]- [13] and the problem of low-thrust transfer and rendezvous of Refs. [6], [15], and [19] extended to the case of continuously varying I sp.
From rocket propulsion fundamentals and using Newton's law for a variable mass body, the equation of motion of a rocket-powered vehicle is given by
where g is the acceleration of gravity, c is the exhaust velocity, and 
is the rate at which...
