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in January 1966
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V. A. Privalov, O. G. Privalova, and V. A. Samsonov, "On the dynamics of a boomerang," Mech. Solids. 38 (4), 28-38 (2003)
Year 2003 Volume 38 Number 4 Pages 28-38
Title On the dynamics of a boomerang
Author(s) V. A. Privalov (Moscow)
O. G. Privalova (Moscow)
V. A. Samsonov (Moscow)
Abstract An elaborate motion of a boomerang has deserved being studied for a long time, and it is astonishing that this has not been carried out so far. The model of [1] that served for illustrating gyroscopic properties of rotating bodies was heuristic rather than rational. In the present paper, we present a theoretical study of the motion of a boomerang. A reasonably complete model of this motion is constructed. The influence of mass, geometrical, and aerodynamic parameters on the character of the calculated trajectories of flight is evaluated. It is shown that this model provides an adequate description of this phenomenon.

A boomerang is a body shaped in such a way that being acted upon by gravity and the incident air flow leads to unexpected original trajectories of the center of mass and a change of the spatial orientation of the boomerang.

Apart from [1], the dynamics of a boomerang is dealt with in [2]. In the latter study, the aerodynamic forces are assumed to be proportional to the linear velocity and the moment of these forces proportional to the angular velocity of the boomerang. However, such a law of aerodynamic action may apply only if the velocity of the motion is relatively low and the air drag is mostly due to viscous friction. Such a hypothesis is hardly can be adopted for the motion of a boomerang.

In contrast to the cited papers, in the present paper, a detailed mathematical model of the motion of a boomerang is constructed.
1.  K. Magnus, A Gyroscope: Theory and Applications [Russian translation], Mir, Moscow, 1974.
2.  A. Gray, A treatise on Gyrostatics and Rotational Motions. Theory and Applications, Macmillan, London, 1918.
3.  V. A. Privalov and V. A. Samsonov, "A comparison of stability properties for two windmilling modes," PMM [Applied Mathematics and Mechanics], Vol. 58, No. 2, pp. 37-48, 1994.
4.  M. L. Mil', A. V. Nekrasov, A. S. Braverman, et al., Helicopters. Calculations and Design. Volume 1. Aerodynamics [in Russian], Mashinostroenie, Moscow, 1966.
5.  B. A. Ushakov, P. P. Krasil'shchikov, A. K. Volkov, and A. N. Grzhegorzhievskii, An Atlas of Airfoils [in Russian], Izd-vo BNT NKAP TsAGI, Moscow, 1940.
Received 17 March 2003
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