Some Necessary Conditions for Time-Optimal,Fixed-Fuel Transfers Between Coplanar Orbits.

摘要

Some necessary conditions in terms of the state and costate variables are derived for time-optimal,thrust-coast-thrust (TCT) trajectories between coplanar, cofocal orbits in an inverse-square gravitational field. Assuming impulsive thrusting,the transfer trajectories are determined by solving a quartic polynomial in the square root of the semi-latus rectum of the transfer orbit. The IBM 7094digital computer was programmed to solve the polynomial and isolate the root leading to the optimal trajectory. Final mass to initial mass ratios are specified,and initial mass is taken as unity. The necessary conditions are derived using plots of constant mass contours in the transfer angle vs. transfer time plane. The conditions are intended to indicate when the TCT trajectory is not optimal and should be replaced by another type of trajectory,such as coast-thrust-coast-thrust (CTCT) or thrust-coast-thrust-coast (TCTC). (Modified author abstract)