Global motion of the celtстатья

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[1] Zhuravlev V. P., Klimov D. M. Global motion of the celt // Mechanics of Solids. — 2008. — Vol. 43, no. 3. — P. 320–327. The motion of the celt attracts researchers' attention by unusual properties. If we put the celt on a horizontal surface and twist it about its vertical axis, then, after a certain time, it stops rotating about this axis, but vibrations about the other axes may arise and then the celt begins rotating about the vertical axis in the opposite direction. Apparently, the first publications about the celt are [1, 2]. The known studies of the celt motion contain some simplifying assumptions and usually perform only a local stability analysis of steady-state rotations. Of the numerous publications, we mention [3, 4], where detailed references can be found. We note that the frequently encountered assumption that the velocity of the celt point of contact with the plane is zero (a nonholonomic statement of the problem) has not been confirmed by physical considerations and must be justified separately. In the present paper, we consider the global motion of the celt for the case in which the interaction of the celt with the plane on which it moves is determined by the forces taking into account the mutually depending sliding and twisting, which makes them really physically meaningful [5]. Another example of application of dry friction model used in the present paper can be found in [6]. [ DOI ]

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