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Representation of light pressure resultant force and moment as a tensor series

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Abstract

In this article, we address the problem of the determination of light pressure upon space structures with a complex geometric shape. For each surface element, we enforce a condition that it can interact with light only from its front side, a condition represented in the form of series of Chebyshev polynomials of the first kind. This Chebyshev expansion enables the use of a series of tensors of increasing rank for determination of the force and moment acting on the sail. We obtain expressions for the determination of light pressure on space structures of complex geometry, taking into account self-shadowing and reflections within the structure. We also give the expressions for tensor parametrization using the specularity coefficient in case of specular -diffuse reflection. For these expressions, we calculated the principal moment and force upon two-sided flat solar sail, spherical and cylindrical bodies, and approximated light pressure upon the proposed space-based observatory Millimetron. The proposed expressions can be used in the ballistic analysis of solar sails and other space objects significantly affected by radiation pressure. Also, these results can be used to analyze the dynamics of large-scale space structures around their center of gravity under light pressure.

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  • 26 October 2017

    In the paper Nerovny et al. (2017), the commentaries about a convergence of series which represent the absolute value function and corresponding equations contain several mistakes (Sect. 2, from Eqs. (4) to (6)).

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Acknowledgements

Authors would like to thank assistant professor Marchevsky I.K. from department “Applied Mathematics” of BMSTU, assistant Kotsur O.S. from department “Aerospace Systems” of BMSTU, and assistant Goncharov D.A. from department “Theoretical Mechanics” of BMSTU for their valuable advice and discussions which led to the creation of the explained method.

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Authors and Affiliations

  1. Bauman Moscow State Technical University, 5 stroenie 1, 2-ya Baumanskaya St., Moscow, Russian Federation, 105005

    Nikolay Nerovny & Vladimir Zimin

  2. Astro Space Center of P.N. Lebedev Physical Institute, 84/32 Profsoyuznaya St., GSP-7, Moscow, Russian Federation, 117997

    Sergey Fedorchuk & Evgeny Golubev

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  1. Nikolay Nerovny
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  2. Vladimir Zimin
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  3. Sergey Fedorchuk
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  4. Evgeny Golubev
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Correspondence to Nikolay Nerovny.

Additional information

This work was prepared during development of BMSTU-Sail Space Experiment Rachkin et al. (2011) and BMSTU-Sail Space Experiment (2014).

A correction to this article is available online at https://doi.org/10.1007/s10569-017-9791-7.

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Nerovny, N., Zimin, V., Fedorchuk, S. et al. Representation of light pressure resultant force and moment as a tensor series. Celest Mech Dyn Astr 128, 483–513 (2017). https://doi.org/10.1007/s10569-017-9758-8

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