 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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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 2022 | Revised |
04 August 2023 | Accepted |
10 August 2023 |
| Link to Fulltext |
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