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IssuesArchive of Issues2023-8pp.2908-2919

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A.D. Chernyshov, M.I. Popov, V.V. Goryainov, and O.Yu. Nikiforova, "Application of the Method of Fast Expansions to Construction of a Trajectory of Movement of a Body with Variable Mass from Its Initial Position in an Achieved Final Position in a Gravitational Field," Mech. Solids. 58 (8), 2908-2919 (2023)
Year 2023 Volume 58 Number 8 Pages 2908-2919
DOI 10.3103/S0025654423080083
Title Application of the Method of Fast Expansions to Construction of a Trajectory of Movement of a Body with Variable Mass from Its Initial Position in an Achieved Final Position in a Gravitational Field
Author(s) A.D. Chernyshov (Voronezh State University of Engineering Technologies, Voronezh, 394000 Russia, chernyshovad@mail.ru)
M.I. Popov (Voronezh State University, Voronezh, 394000 Russia)
V.V. Goryainov (Voronezh State Technical University, Voronezh, 394000 Russia)
O.Yu. Nikiforova (Voronezh State University of Engineering Technologies, Voronezh, 394000 Russia)
Abstract An analytical solution of the problem of the movement of a spacecraft from the starting point to the final point in a certain time is given. First, the method of fast sine expansions is used. The space problem considered here is essentially nonlinear, which necessitates the use of trigonometric interpolation methods that surpass all known interpolations in accuracy and simplicity. In this case, the problem of calculating Fourier coefficients by integral formulas is replaced by the solution of an orthogonal interpolation system. In this regard, two cases are considered on the segment [0, a]: universal interpolation and trigonometric sine and cosine interpolations. A theorem on the rapid decrease of expansion coefficients is proved, and a compact formula for calculating the interpolation coefficients is obtained. A general theory of fast expansions is given. It is shown that, in this case, the Fourier coefficients decrease significantly faster with the growth of the ordinal number compared to the Fourier coefficients in the classical case. This property makes it possible to significantly reduce the number of terms taken into account in the Fourier series, significantly increase the accuracy of calculations, and reduce the amount of calculations on a computer. An analysis of the obtained solutions of the spacecraft motion problem is carried out, and their comparison with the exact solution of the test problem is proposed. An approximate solution by the method of fast expansions can be taken as an exact one, since the input data of the problem used from reference books have a higher error.
Keywords gravity field, body of variable mass, spacecraft, fast expansions method, fast trigonometric interpolation
Received 28 September 2022Revised 04 August 2023Accepted 10 August 2023
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