Space Flight Mechanics Laboratory

As a result of the work carried out, a program library was developed that allows calculating the first and mixed second derivatives of real functions of several variables with an accuracy close to the accuracy of calculating functions. The developed software library was used as part of the software for optimizing the perturbed trajectories of spacecraft. For the created programs, a certificate of state registration of the computer program was obtained. A new numerical method for solving the fuel minimization problem for perturbed multi-turn trajectories with finite thrust is developed based on the use of the maximum principle, the continuation method, and complex-dual algebra for the exact calculation of the required derivatives. The theoretical analysis of the basic properties of optimal pulse trajectories is carried out and based on them, the theoretical foundations for the continuation of the optimal trajectory of a spacecraft with a perfectly controlled engine into the optimal pulse trajectory are developed.

The dynamics of the spatial motion of a passive object transported under the influence of an ion beam is studied. A mathematical model describing the spatial motion of a passive object under the action of an ion flux is developed. Simplified models describing the motion of an object with a small asymmetry and an axisymmetric object in a geostationary orbit are developed. The law of ion beam control is developed, which ensures the stabilization of the spatial motion of a passive object in the mode of regular precession. Experimental work was carried out to determine the accommodation coefficient of the ion pulse and the force acting on the target when it is irradiated with an ion beam at different angles. It is established that the force acting on the target, within the statistical error, does not depend on the angle of the target installation.

Implemented results of research:

Developed computer programs for which certificates of state registration were obtained:

1. V.G. Petukhov "Program for optimizing perturbed spacecraft trajectories using the algebra of complex-dual numbers". Certificate of state registration of the computer program No. 2020619491 of 8.08.2020.
2. M.S. Konstantinov, I. A. Nikolichev "A program for determining the parameters of the trajectory of the passive movement of the center of mass of the returned rocket, making a flight from a given point on the surface of the moon to the Earth". Certificate of state registration of the computer program No. 2020663242 dated 26.10.2020.

The results of the research were presented at international and all-Russian conferences and were used in the execution of works commissioned by space industry enterprises for space mission design and trajectory analysis.