AAS 97-716
MINIMUM TIME TRANSFER OF A CONSTANT LOW THRUST ROCKET BETWEEN ELLIPTIC ORBITS IN STRONG NEWTONIAN GRAVITY FIELDS
B.N. Kiforenko, Z.V. Pasechnik and I.Y. Vasiliev - Kiev Taras Schevchenko University L.R. Balkanyi and J.P. Riehl - NASA Lewis Research Center
Abstract
The problem under consideration is minimum time transfer of a low thrust space vehicle between elliptic orbits in strong central gravitational fields. The thrust of the rocket is assumed to be constant in magnitude and controllable in direction. The positions of the vehicle in both initial and final orbits are unspecified in the sense that anomaly is not considered.
Taking into account the specific peculiarities of the trajectories with a large number of revolutions around the attracting central body, an algorithm for optimal trajectory calculation is developed. The algorithm has an hierarchical structure and is developed with the use of linearization of the equations of motion in an "inner" problem and the substitution of a discrete independent variable for a continuous one in an "outer" problem.
The analytic solution is obtained for the linear approximation of the "inner" problem. The possibility of an analytic solution of the "outer" problem is investigated.
Taking advantage of a newly obtained first integral, along with the use of well known first integrals, the "outer problem" is reduced to a form which requires numerical integration of a differential system of fourth order as well as the determination of the four constants of integration from the boundary conditions.
The analytic solutions are also obtained for the maneuvres which simultaneously change both the shape of an elliptic orbit and one of the angles which defines its orientation in space.