About the First Integral in the Classical Problem of External Ballistics

B. Ya. Lokshin; Локшин Б. Я.; V. A. Samsonov; Самсонов В. А.

doi:10.31857/S0032823524020024

About the First Integral in the Classical Problem of External Ballistics

Authors: Lokshin B.Y.¹, Samsonov V.A.¹
Affiliations:
1. Lomonosov Moscow State University
Issue: Vol 88, No 2 (2024)
Pages: 190-197
Section: Articles
URL: https://rjonco.com/0032-8235/article/view/675062
DOI: https://doi.org/10.31857/S0032823524020024
EDN: https://elibrary.ru/XVFMFK
ID: 675062

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Abstract

The transcendental first integral of the classical problem of external ballistics has been retrieved from oblivion. A change of variables was proposed that transformed the integral to a compact form. This allowed for reducing the solution of the problem to constructive quadratures.

Keywords

external ballistics, first integral, new variables, phase portrait

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About the authors

B. Ya. Lokshin

Lomonosov Moscow State University

Author for correspondence.
Email: blokshin@imec.msu.ru
Russian Federation, Moscow

V. A. Samsonov

Lomonosov Moscow State University

Email: samson@imec.msu.ru
Russian Federation, Moscow

References

Leonhard Euler. Ballistics Studies. Moscow: GIFML, 1961. 590 p. (in Russian)
Lokshin B.Ya., Samsonov V.A. The Problem of the Motion of a Body in a Resisting Medium. Qualitative Analysis. Moscow: MSU, 2012. (in Russian)
Appell P. Theoretical Mechanics. Vol. 1. Moscow: Fizmatlit, 1960.
Chernozubov A.D., Kirichenko V.D., Razin I.I. et al. External Ballistics. Vol. 1. Moscow: Dzerzhinsky VAIA Pub., 1954. 463 p.
Guskov A.V., Milevsky K.E., Sotenko A.V. External Ballistics. Novosibirsk: NSTU Pub., 2010. 188 p.
Lokshin B.Ya., Samsonov V.A. On the approximation of the flight path of a ballistic object // Izv. RA RAN, 2023, no. 3, pp. 38–43.