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As of 15.02.2021

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scientific publications
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General information
Name of the project: Space flight mechanics

Strategy for Scientific and Technological Development Priority Level: е

Goals and objectives
Project objective: Development of theoretical basics and methods of space flight mechanics necessary for modernization of existing and creation of principally new models of rocket and space units for design of prospective space systems

The practical value of the study

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.

Education and career development:

The advanced training program "Mechanics of space flight"was developed and implemented in the educational activities at the Department 601 of the MAI.


Samara Scientific Center of the Russian Academy of Sciences (Russia): collaborative research.

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Aslanov V., Ledkov A., Konstantinov M.
Chaotic motion of a cylindrical body during contactless transportation from MEO to LEO by ion beam // Nonlinear Dynamics, 2020, Т 101, № 2, c. 1221-1231.
Aslanov V. S., Ledkov A. S., Konstantinov M. S.
Attitude motion of a space object during its contactless ion beam transportation // Acta Astronautica, 2021, Т 179, c. 359-370.
Obukhov, V.A., Kirillov, V.A., Petukhov, V.G., Popov, G.A., Svotina, V.V., Testoyedov, N.A., Usovik, I.V.
Problematic issues of spacecraft development for contactless removal of space debris by ion beam // Acta Astronautica, 2021, DOI: 10.1016/j.actaastro.2021.01.043.
Petukhov V.G., Ivanyukhin A.V., Popov G.A., N. Testoyedov, Sung Wook Yoon
Optimization of finite-thrust trajectories with fixed angular distance // Acta Astronautica, 2021, DOI: 10.1016/j.actaastro.2021.03.012.
Petukhov V.G., Ivanyukhin A.V.
Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable // Journal of optimization theory and applications, 2021, DOI: 10.1007/s10957-021-01853-8
Popov, G., Aslanov, V., Petukhov, V., Ledkov, A.
Influence of space debris attitude motion on ion beam assisted removal mission costs, 2020, Proceedings of the International Astronautical Congress, IAC, 2020-October.
Aslanov, V., Ledkov, A., Konstantinov, M.
Attitude dynamics and control of space object during contactless transportation by ion beam, 2020, Proceedings of the International Astronautical Congress, IAC, 2020-October.
Petukhov, V.G.
A new approach to low-thrust perturbed trajectory optimization based on the use of complex dual numbers, 2020, Proceedings of the International Astronautical Congress, IAC, 2020-October.
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