Abstract
The first integrals of the dynamic part of the equations of the axially symmetric solid body moving in a resisting medium in the presence of an additional tracking force were listed completely. In the sense of complex analysis, the first integrals are the transcendental functions of their variables expressed in terms of a finite combination of the elementary functions.
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Samsonov, V.A. and Shamolin, M.V., On the Problem of Body Motion in a Resisting Medium, Vestn. Mosk. Univ., Ser. 1: Mat. Mekh., 1989, no. 3, pp. 51–55.
Shamolin, M.V., Metody analiza dinamicheskikh sistem s peremennoi dissipatsiei v dinamike tverdogo tela (Methods for Analysis of Dynamic Systems with Variable Dissipation in the Solid Body Dynamics), Moscow: Ekzamen, 2004.
Chaplygin, S.A., On Motion of Heavy Bodies in Incompressible Liquid, in Complete Works, Leningrad: Akad. Nauk SSSR, 1933, vol. 1, pp. 133–135.
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Original Russian Text © M.B. Shamolin, 2013, published in Avtomatika i Telemekhanika, 2013, No. 8, pp. 173–190.
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Shamolin, M.B. A new case of integrability in transcendental functions in the dynamics of solid body interacting with the environment. Autom Remote Control 74, 1378–1392 (2013). https://doi.org/10.1134/S0005117913080146
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DOI: https://doi.org/10.1134/S0005117913080146