Abstract
A mathematical model of the influence of a medium on a rigid body with some part of its external surface being flat is considered with due allowance for an additional dependence of the moment of the medium action force on the angular velocity of the body. A full system of equations of motion is given under quasi-steady conditions; the dynamic part of this system forms an independent third-order system, and an independent second-order subsystem is split from the full system. A new family of phase portraits on a phase cylinder of quasi-velocities is obtained. It is demonstrated that the results obtained allow one to design hollow circular cylinders (“shell cases”), which can ensure necessary stability in conducting additional full-scale experiments.
Similar content being viewed by others
References
N. E. Joukowski, “Incidence of Light Extended Bodies Rotating around their Longitudinal Axis,” in Total Collected Papers (Fizmatgiz, Moscow, 1937), Vol. 5, pp. 72–80 and 100–115) [in Russian].
S. A. Chaplygin, Selected Papers (Nauka, Moscow, 1976) [in Russian].
S. A. Chaplygin, “On Motion of Heavy Bodies in an Incompressible Fluid,” in Total Collected Papers (Izd. Akad. Nauk SSSR, Leningrad, 1933), Vol. 1, pp. 133–135 [in Russian].
M. V. Shamolin, Methods of Analysis of Variable Dissipation Dynamic Systems in Rigid Body Dynamics (Ekzamen, Moscow, 2007) [in Russian].
M. V. Shamolin, “Dynamic Systems with Variable Dissipation: Approaches, Methods, and Applications,” Fundam. Prikl. Mat. 14 (3), 3–237 (2008).
H. Lamb, Hydrodynamics (Cambridge Univ. Press, Cambridge, 1932).
M. V. Shamolin, “Variety of Integrable Cases in Dynamics of Low- and Multi-Dimensional Rigid Bodies in Nonconservative Force Fields,” Itogi Nauki Tekh., Ser. Sovr. Mat. Pril. Temat. Obzory 125, 3–251 (2013).
B. Ya. Lokshin, V. A. Privalov, and V. A. Samsonov, Introduction into the Problem of Motion of a Body in a Resisting Medium (Izd. Mosk. Gos. Univ., Moscow, 1986) [in Russian].
V. A. Eroshin, G. A. Konstantinov, N. I. Romanenkov, and Yu. L. Yakimov, “Experimental Determination of Pressure on a Disk Submerged into a Compressible Fluid at an Angle to the Free Surface,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 21–25 (1988).
V. A. Eroshin, G. A. Konstantinov, N. I. Romanenkov, and Yu. L. Yakimov, “Experimental Determination of the Moment of Hydrodynamic Forces in the Case of Asymmetric Penetration of a Disk into a Compressible Fluid,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 88–94 (1990).
M. I. Gurevich, Theory of Jets of an Ideal Fluid (Nauka, Moscow, 1979) [in Russian].
V. G. Tabachnikov, Steady-State Characteristics of Wings at Small Velocities in the Entire Range of the Angles of Attack,” Tr. TsAGI, No. 1621, 18–24 (1974).
L. Prandtl and A. Betz, Ergebmisse der Aerodinamischen Versuchsastalt zu Gottingen (Aerodinam. Versuchsastalt zu Gottingen, München–Berlin, 1932).
G. S. Bushgens and R. V. Studnev, Aircraft Dynamics. Spatial Motion (Mashinostroenie, Moscow, 1988) [in Russian].
V. A. Eroshin, V. A. Samsonov, and M. V. Shamolin, “Model Problem of Body Deceleration in a Resisting Medium in a Jet Flow,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 3, 23–27 (1995).
V. A. Samsonov, M. V. Shamolin, V. A. Eroshin, and V. M. Makarshin, “Mathematical Modeling in the Problem of Body Deceleration in a Resisting Medium in a Jet Flow,” Report No. 4396 (Inst. Mechanics, Moscow State University, Moscow, 1995).
V. A. Eroshin, “Experimental Study of High-Velocity Penetration of an Elastic Cylinder into Water,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 5, 20–30 (1992).
Yu. K. Bivin, V. V. Viktorov, and L. P. Stepanov, “Study of the motion of a Rigid Body in a Clay Medium,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 159–165 (1978).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 57, No. 4, pp. 43–56, July–August, 2016.
Rights and permissions
About this article
Cite this article
Shamolin, M.V. On the problem of free deceleration of a rigid body in a resisting medium. J Appl Mech Tech Phy 57, 611–622 (2016). https://doi.org/10.1134/S0021894416040052
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894416040052