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Procedings of the 2nd International Conference "Mathematical Physics and its Applications"
Mechanics
Stability of disk motion on the rheological ground
G. V. Pavlov, M. A. Kal'mova, E. S. Vronskaya, I. N. Ignatov Dept. of Resistance of Materials and Construction Mechanics, Samara State Academy of Architecture and Construction, Samara
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
In this paper a new mathematical model of the disk motion on the basis of the Kelvin body is constructed. Taking the hypothesis of a point contact with the drive base, a system of differential equations of the disk motion is derived in the form of modified Chaplygin equations involving generalized rheological response force, as well as three stationary constraint equations, two of which are nonholonomic. The analysis of the drive permanent movements stability was carried out. It is shown that the rectilinear motion of the disk and spinning around a vertical diameter are unstable in relation to the nutation angle $\theta$.
Keywords:
nonholonomic connection, relaxation curve, Mikhailov hodograph.
Original article submitted 20/XII/2010 revision submitted – 19/I/2011
Citation:
G. V. Pavlov, M. A. Kal'mova, E. S. Vronskaya, I. N. Ignatov, “Stability of disk motion on the rheological ground”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(23) (2011), 306–312
Linking options:
https://www.mathnet.ru/eng/vsgtu882 https://www.mathnet.ru/eng/vsgtu/v123/p306
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Abstract page: | 395 | Full-text PDF : | 241 | References: | 67 | First page: | 1 |
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