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A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2019-3pp.429-434

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K.Yu. Osipenko, "Stability of Rectilinear Motion of a Cone Rotating Around the Axis of Symmetry," Mech. Solids. 54 (3), 429-434 (2019)
Year 2019 Volume 54 Number 3 Pages 429-434
DOI 10.3103/S0025654419020067
Title Stability of Rectilinear Motion of a Cone Rotating Around the Axis of Symmetry
Author(s) K.Yu. Osipenko (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Moscow State University of Civil Engineering, Yaroslavskoye sh. 26, Moscow, 129337 Russia, kirill-o@mail.ru)
Abstract The effect of constant friction on the stability of the rectilinear motion of a cone rotating around the axis of symmetry is considered. It is assumed that the lateral surface of the cone is seamlessly streamlined and that normal stresses and friction act on this surface, which are determined by the method of local interaction. Normal contact stresses are assumed to be proportional to the square of the normal velocity component, and friction is assumed to be constant modulo and acting in the direction of the inverse projection of the velocity vector onto the tangent plane. For frozen velocities of the center of mass and angular velocity of rotation around the axis of symmetry, asymptotic stability criteria are obtained in the form of a system of two inequalities that does not contain integrals. The effect of friction on the stability of the rectilinear motion of a homogeneous cone is studied in detail.
Keywords penetration, trajectory, rotation around the axis of symmetry, stability
Received 12 October 2017
Link to Fulltext https://link.springer.com/article/10.3103/S0025654419020067
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