Mathematical Models and Computer Simulations

, Volume 10, Issue 2, pp 226–236 | Cite as

The Restoration of Input Parameters of an Exterior Ballistic Solution by the Results of Body Movement Trajectory Measurement

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Abstract

Analyzing the results of ballistic experiments often brings up the problem of restoring the input computation parameters of the exterior ballistics of a body (the ballistic coefficient, the initial velocity, the environment temperature, the pressure, etc.) by the results of trajectory measurements (the reverse problem of exterior ballistics). It is found that without a priori information on unknown parameters, the problem in question cannot have a unique solution. We propose a procedure of solving the reverse problem with a priori information at hand; this procedure rests on the least-squares method and the maximum-likelihood method. An algorithm for solving the reverse problem is described in detail (the described algorithm implements the proposed procedure). We consider applying this procedure to the problem of restoring the initial departure conditions and atmospheric parameters, as well as to the problem of simultaneously determining the initial velocity of the body and its ballistic coefficient.

Keywords

reverse problem exterior ballistics experimental ballistics numerical methods maximumlikelihood method least-squares method 

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References

  1. 1.
    A. M. Denisov, Elements of the Theory of Inverse Problems, Vol. 14 of Inverse and Ill-Posed Problems Series (Mosk. Gos. Univ., Moscow, 1994; Walter de Gryuter, Berlin, Boston, 1999).Google Scholar
  2. 2.
    V. G. Romanov, Inverse Problems of Mathematical Physics (Nauka, Moscow, 1984) [in Russian].MATHGoogle Scholar
  3. 3.
    A. N. Tikhonov, A. S. Leonov, and A. G. Yagola, Nonlinear Incorrect Problems (Nauka, Fizmatlit, Moscow, 1995) [in Russian].MATHGoogle Scholar
  4. 4.
    A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems (Moscow, Nauka, 1986; Halsted, New York, 1977).MATHGoogle Scholar
  5. 5.
    A. S. Leonov, Solution of Ill-Posed Inverse Problems: Theory Essay, Pratical Algorithms and Demonstrations in MATLAB (LIBROKOM, Moscow, 2010) [in Russian].Google Scholar
  6. 6.
    N. N. Kalitkin and E. A. Alshina, Numerical Methods, Vol. 1: Numerical Analysis (Akademiya, Moscow, 2013) [in Russian].Google Scholar
  7. 7.
    G. I. Ivchenko and Yu. I. Medvedev, Mathematical Statistics, The School-Book for Higher Technical Schools (Vyssh. Shkola, Moscow, 1984) [in Russian].Google Scholar
  8. 8.
    A. A. Konovalov and Yu. V. Nikolaev, External Ballistics (TsNII Inform., Moscow, 1979) [in Russian].Google Scholar
  9. 9.
    V. V. Burlov et al., Ballistics of Barrel Systems, Ed. by L. N. Lysenko and A. M. Lipanov (Mashinostroenie, Moscow, 2006) [in Russian].Google Scholar
  10. 10.
    E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, 2nd ed. (Springer, Berlin, Heidelberg, 1996).MATHGoogle Scholar
  11. 11.
    N. N. Kalitkin and P. V. Koryakin, Numerical Methods, Vol. 2: Mathematical Physics Methods (Akademiya, Moscow, 2013) [in Russian].Google Scholar
  12. 12.
    I. A. Kozlitin and A. S. Omel’yanov, “Smooth approximation of drag force-body speed relation,” Elektron. Inform. Sist., No. 6, 90–100 (2015).Google Scholar
  13. 13.
    A. E. Bondarev and V. A. Galaktionov, “Multidimensional data analysis and visualization for time-dependent CFD problems,” Program. Comput. Software 41, 247 (2015).MathSciNetCrossRefGoogle Scholar
  14. 14.
    Manual on 12.7-mm Machine Gun Utes NSV-12.7 (Voen. Izdat., Moscow, 1986) [in Russian].Google Scholar
  15. 15.
    Ya. M. Shapiro, External Ballistics (Oborongiz, Moscow, 1946) [in Russian].Google Scholar
  16. 16.
    http://www.ntiim.ru/info.php?x=rush.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia

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