ИСТИНА

The actual optimization problem of nonplanar space transfer of the spacecraft (SC) to Phobos is considered [1]. In the first version of the Phobos-Grunt project the SC with a combined propulsion system comprising jet engines of the low thrust (LT) was supposed to use [2]. Maneuvers near Mars and return stage were implemented with the use of engine of the big thrust (BT). Later perspective scheme with combining BT and LT jet engines was rejected, however, the problem of design and optimizing the combined propulsion schemes of interplanetary missions remains. Such problems are known for a long time [3]. Effectiveness of using LT in interplanetary expeditions is well known. We suppose that the SC starts from the artificial Earth satellite orbit corresponding to start from Baikonur since 2020 to 2030 years and arrives to Phobos in some time. Total duration of an expedition is limited. The coordinates of the Earth, Mars and Phobos correspond to ephemeris DE424 and MAR097. Gravitational fields of the Sun, the Earth and Mars are considered to be Newtonian. The SC and Phobos are supposed to be non-attracting material points, their coordinates and velocity vector in the final moment are equal. The moments of the SC start and finish are optimized. The SC is equipped with BT and LT jet engines. The control is realized by the value and the direction of a jet thrust vector. After the end of the each propulsion system using trajectory part, it is instantly dumping. The SC angular position on an initial starting circle, the moments of thrust inclusion and switching off are optimized. Weight losses are minimized. The problem of cosmodynamics is formalized as an optimal control problem of set of dynamic systems and decides on the basis of the Pontryagin’s maximum principle. The six-dot boundary value problem reduces down to point-to-point problem and is solved numerically with the use of shooting method. The external gradient methods optimization are used in extremal creating. One of the difficulties which researcher have to overcome during the decision creation is the restructuring of trajectory. Through task parameters optimization is made. The possible prize of using the combined thrust in comparison with using only BT engines is estimated. Specific numerical results are given. Consideration of the complex trajectory optimization problems demanding the synthesis of local and multiextremal optimization methods, optimal control, cosmodynamics, mechanics of space flight, gravitational astronomy and numerical methods, gives the significant contribution to the solution of such problems theory. REFERENCES [1] The space mission project. Scientific publication in two volumes. Vol. 1, 2. Moscow, Federal State Unitary Enterprise “NPO. SA Lavochkin” Roscosmos, the Russian Academy of Sciences Space Research Institute, 2011, 519 p. [2] Avduevsky V.S., Akim E.L., Kremnev R.S., Kulikov S.D. Space project “Phobos–Grunt”: main characteristics and development of strategy. Kosmonavtika i raketostroenie, 2000, vol. 19, pp. 8–21. [3] Edelbaum T. N. The Use of High- and Low-Thrust Propulsion in Combination for Space Missions. Journal of the Astronautical Sciences, 1962, vol. 9, no. 2, pp. 49-69.