Geodesic
Approximation by elementary functions for the solution of meteor physics equations
Matematičeskoe modelirovanie, Tome 27 (2015) no. 2, pp. 25-33.

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In this paper we examine the possibility of approximation by elementary functions for the analytical solution of meteor physics equations, used to describe the trajectory and to evaluate the defining parameters of meteoroids entering the Earth's atmosphere. We show the possibility to replace the analytical solution with the concatenation of two elementary functions along one parameter. We provide estimates for the error of the proposed replacement. We investigate the error functional value in the approximation of meteor observational data.
Keywords: exponential integral, analytical solution, approximation, atmospheric trajectory, meteor, deceleration
Mots-clés : ablation. 
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M. I. Gritsevich; V. T. Lukashenko; L. I. Turchak. Approximation by elementary functions for the solution of meteor physics equations. Matematičeskoe modelirovanie, Tome 27 (2015) no. 2, pp. 25-33. http://geodesic.mathdoc.fr/item/MM_2015_27_2_a1/

[1] M. I. Gritsevich, “Determination of Parameters of Meteor Bodies based on flight Observational Data”, Advances in Space Research, 44 (2009), 323–334 | DOI

[2] M. I. Gritsevich, “Identification of Fireball Dynamic Parameters”, Moscow University Mechanics Bulletin, 63:1 (2008), 1–5 | DOI

[3] G. W. Wetherill, D. O. ReVelle, “Which fireballs are meteorites — A study of the Prairie Network photographic meteor data”, Icarus, 48 (1981), 308–328 | DOI

[4] I. Halliday, A. A. Griffin, A. T. Blackwell, “Detailed data for 259 fireballs from the Canada camera network and inferences concerning the influx of large meteoroids”, Meteoritics Planetary Science, 31 (1996), 185–217 | DOI

[5] M. I. Gritsevich, “Approximation of the Observed Motion of Bolides by the Analytical Solution of the Equations of Meteor Physics”, Solar System Research, 41:6 (2007), 509–514 | DOI

[6] N. N. Kalitkin, I. A. Panin, “On the Computation of the Exponential Integral”, Mathematical Models and Computer Simulations, 1:1 (2009), 88–90 | DOI

[7] V. V. Vinnikov, M. I. Gritsevich, V. T. Lukashenko, “Traektoriia i orbitalnye kharakteristiki Cheliabinskogo meteoroida”, Sb. tezisov dokladov nauchnoi konferentsii “Lomonosovskie chteniia”, Sektsiia mekhaniki, Izd. Moskovskogo universiteta, M., 2013, 34–36

[8] M. I. Gritsevich, “The Pribram, Lost City, Innisfree, and Neuschwanstein Falls: An analysis of the Atmospheric Trajectories”, Solar System Research, 42:5 (2008), 372–390 | DOI

[9] R. J. Weryk, P. G. Brown, A. Domokos, W. N. Edwards, Z. Krzeminski, S. H. Nudds, D. L. Welch, “The Southern Ontario All-sky Meteor Camera Network”, Earth, Moon, and Planets, 102 (2008), 241–246 | DOI

[10] P. Jenniskens, P. S. Gural, L. Dynneson, B. J. Grigsby, K. E. Newman, M. Borden, M. Koop, D. Holman, “CAMS: Cameras for Allsky Meteor Surveillance to establish minor meteor showers”, Icarus, 216:1 (2011), 40–46 | DOI

[11] J. Kero, C. Szasz, T. Nakamura, D. D. Meisel, M. Ueda, Y. Fujiwara, T. Terasawa, K. Nishimura, J. Watanabe, “The 2009–2010 MU radar head echo observation programme for sporadic and shower meteors: radiant densities and diurnal rates”, Monthly Notices of the Royal Astronomical Society, 425:1 (2012), 135–146 | DOI

[12] J. Gural, “A Meteor Propagation Model based on Fitting the Differential Equations of Meteor Motion”, Proceedings of the International Meteor Conference 2012, eds. M. Gyssens, P. Roggemans, International Meteor Organization, 130–132

[13] V. P. Stulov, V. N. Mirskii, A. I. Vislyi, Aerodinamika bolidov, Nauka. Fizmatlit, M., 1995, 236 pp.

[14] M. I. Gritsevich, N. V. Popelenskaya, “Meteor and Fireball Trajectories for High Values of the Mass Loss Parameter”, Doklady Physics, 53:2 (2008), 88–92 | DOI

[15] N. V. Popelenskaia, “Zavisimost vysoty pogasaniia malykh meteornykh tel ot ikh parametrov”, Vestnik MGU, ser. 1, Matematika, mekhanika, 2010, no. 4, 65–68

[16] A. E. Dubinov, I. D. Dubinova, S. K. Saikov, W-funktsiia Lamberta i ee primenenie v matmaticheskikh zadachakh fiziki, FGUP «RFIaTs-VNIIEF», Sarov, 2006, 160 pp.