Geodesic
The restoration of input parameters of an exterior ballistic solution by the results of body movement trajectory measurement
Matematičeskoe modelirovanie, Tome 29 (2017) no. 9, pp. 121-134.

Voir la notice de l'article provenant de la source Math-Net.Ru

The restoration of input parameters of an exterior ballistic solution (drag coefficient, initial velocity, temperature, pressure and other) by the results of body movement trajectory measurement is an important problem for analyzing of results of ballistic experiments (reverse exterior ballistic problem). It was established that without a priori information about unknown parameters, it does not have a single solution. A method is proposed for the solution of the reverse exterior ballistic problem with a priori information available on the base of the least-squares method and the maximum-likelihood method. The algorithm for solving this problem is described in detail. It was used for restoration of initial throwing conditions and atmosphere parameters and for solving problem of restoration of an initial velocity and a drag coefficient at the same time.
Keywords: reverse problem, exterior ballistic, experimental ballistic, numerical methods, maximum-likelihood method, least-squares method. 
@article{MM_2017_29_9_a9,
     author = {I. A. Kozlitin},
     title = {The restoration of input parameters of an exterior ballistic solution by the results of body movement trajectory measurement},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {121--134},
     publisher = {mathdoc},
     volume = {29},
     number = {9},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_9_a9/}
}
TY  - JOUR
AU  - I. A. Kozlitin
TI  - The restoration of input parameters of an exterior ballistic solution by the results of body movement trajectory measurement
JO  - Matematičeskoe modelirovanie
PY  - 2017
SP  - 121
EP  - 134
VL  - 29
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2017_29_9_a9/
LA  - ru
ID  - MM_2017_29_9_a9
ER  - 
%0 Journal Article
%A I. A. Kozlitin
%T The restoration of input parameters of an exterior ballistic solution by the results of body movement trajectory measurement
%J Matematičeskoe modelirovanie
%D 2017
%P 121-134
%V 29
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2017_29_9_a9/
%G ru
%F MM_2017_29_9_a9
I. A. Kozlitin. The restoration of input parameters of an exterior ballistic solution by the results of body movement trajectory measurement. Matematičeskoe modelirovanie, Tome 29 (2017) no. 9, pp. 121-134. http://geodesic.mathdoc.fr/item/MM_2017_29_9_a9/

[1] Denisov A. M., Vvedenie v teoriiu obratnykh zadach, Izd-vo MGU, M., 1994, 207 pp.

[2] Romanov V. G., Obratnye zadachi matematichesko fiziki, Nauka, M., 1984, 261 pp.

[3] Tikhonov A. N., Leonov A. S., Iagola A. G., Nelineinye nekorrektnye zadachi, Nauka. Fizmatlit, M., 1995, 312 pp.

[4] Tikhonov A. N., Arsenin V. Ia., Metody resheniia nekorrektnykh zadach, Nauka, M., 1986, 287 pp. | MR

[5] Leonov A. S., Reshenie nekorrektno postavlennykh obratnykh zadach: Ocherk teorii, prakticheskie algoritmy i demonstratsii v MATLAB, Knizhny dom LIBROKOM, M., 2010, 336 pp.

[6] Kalitkin N. N., Alshina E. A., Chislennye metody, V 2 kn., v. 1, Chislenny analiz, Akademiia, M., 2013, 304 pp.

[7] Ivchenko G. I., Medvedev Iu. I., Matematicheskaia statistika, Ucheb. Posobie dlia vtuzov, Vyssh. shk., M., 1984, 248 s., il. pp.

[8] Konovalov A. A., Nikolaev Iu. V., Vneshniaia ballistika, TsNII informatsii, M., 1979, 228 pp.

[9] Burlov V. V. i dr., Ballistika stvolnykh sistem, eds. L.N. Lysenko, A.M. Lipanov, Mashinostroenie, M., 2006, 461 pp.

[10] Hairer E., Wanner G., Solving Ordinary Differential Equations, v. Stiff and Differential-Algebraic Problems, Second Revised Edition, Springer, 1996 | MR | Zbl

[11] Kalitkin N. N., Koriakin P. V., Chislennye metody, V 2 kn., v. 2, Metody matematichesko fiziki, Akademiia, M., 2013, 304 pp.

[12] Kozlitin I. A., Omelianov A. S., “Gladkaia approksimatsiia zavisimosti sily lobovogo soprotivleniia ot skorosti dvizheniia tela”, Elektronnye informatsionnye sistemy, 2015, no. 3(6), 90–100

[13] Bondarev A. E., Galaktionov V. A., “Analiz i vizualizatsiia mnogomernykh dannykh v nestatsionarnykh zadachakh vychislitelno gazovo dinamiki”, Programmirovanie, 2015, no. 5, 5–12

[14] Rukovodstvo po 12,7-mm pulemetu Utes (NSV-12,7), Voennoe izdatelstvo, M., 1986 | Zbl

[15] Shapiro Ia. M., Vneshniaia ballistika, Oborongiz, M., 1946, 408 pp.

[16] http://www.ntiim.ru/info.php?x=rush