TABLE OF CONTENTS A discussion of the problem of optimal low-thrust transfer between inclined circular orbits was presented by Edelbaum in the early 1960s. [1] Assuming constant acceleration and constant thrust vector yaw angle within each revolution, Edelbaum linearizes the Lagrange planetary equations of orbital motion about a circular orbit and, using the velocity as the independent variable, reduces the transfer optimization problem to a problem in the theory of maxima. The variational integral involves a single constant Lagrange multiplier since it involves a single integral constraint equation for the transfer time or velocity change while maximizing the change in orbital inclination. The control variable being the yaw angle, the necessary condition for a stationary solution is obtained by simply setting the partial derivative of the integrand of the variational integral with respect to the control to zero. This optimum control is then used in the right-hand sides of the original equations of motion, which are integrated analytically to provide expressions for the time and inclination in terms of the independent variable, the orbital velocity. Two expressions for the inclination are provided to cover the case of large inclination change transfers. This complication arises if orbital velocity is adopted as the independent variable. However, a single expression for the inclination change can be obtained that is uniformly valid throughout any desired transfer if the original Edelbaum problem is cast into a minimum-time transfer problem using the more direct formalism of optimal control theory. Following is a...
