Generalized Hohmann, Bi-Parabolic and Bi-Elliptic Planar Impulsive Transfer Using Transformed Variables

Abstract

The problem of planar optimal impulsive transfer between ellipses in a Newtonian gravitational field with the final time- free is approached through a transformation of variables. New necessary conditions for optimal Bi-Elliptic Transfers are presented in terms of these transformed variables. The work is applied to examples in which the apses of the ellipses are aligned. The Generalized Hohmann, Bi-Elliptic and Bi-Parabolic Transfers are discussed. An example is presented that shows that Bi-Elliptic Transfer cannot be optimal if the final time is free. The approach can also be applied to determine optimality of transfers for other aligned configurations. This project is then changed to a fixed final time minimization problem. For this problem, it is found that there is a one-to-one correspondence between the final time and the apogee of the transfer ellipse. It is shown from this fact that there can be optimal Bi-Elliptic Transfers if the final time is fixed.