Abstract
One of the classical contact problems of two-dimensional chain dynamics for the cases without friction and with dry friction is considered. An analytical formula for tension of the chain along its total length is found in the paper. The conditions for disappearance of the chain contact with the support are considered. The existence of the energy integral gives the possibility to obtain these conditions in an analytical way. In the case with friction, numerical-analytical results of the investigation are given.
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REFERENCES
P. G. Tait and W. J. Steel, A Treatise on the Dynamics of a Particle, 2nd ed. (Macmillan, Cambridge, 1865).
A. E. H. Love, Theoretical Mechanics (an Introductory Treatise on the Principles of Dynamics) (Cambridge Univ. Press, Cambridge, 1897).
J. H. Jeans, An Elementary Treatise on Theoretical Mechanics (GINN, Boston, 1907).
H. Lamb, Dynamics (Cambridge Univ. Press., Cambridge, 1961).
E. J. Routh, Dynamics of a System of Rigid Bodies, 6th ed. (Macmillan, New York, 1905), Part 2.
P. Appell, Traité de Mécanique Rationnelle, Vol. 2: Dynamique des Systèmes. Mécanique Analytique, 6th ed. (Gauthier-Villar, Paris, 1953).
G. Hamel, Theoretische Mechanik. Grundlehren der Mathematischen Wissenschaften (Springer-Verlag, Berlin, 1967), Vol. 57.
A. Cayley, “On a class of dynamical problems,” Proc. R. Soc. London 8, 506–511 (1857).
O. M. O’Reilly, Modeling Nonlinear Problems in the Mechanics of Strings and Rods (the Role of the Balance Laws) (Springer-Verlag, New York, 2017).
E. Lainé, Exercices de Mécanique (Librarie Vuibert, Paris, 1964).
R. Sanmartin Juan and A. Vallejo Miguel, “Widespread error in a standard problem in the dynamics of deformable bodies,” Am. J. Phys. 46 (9), 949–950 (1978).
D. Prato and R. J. Gleiser, “Another look at the uniform rope sliding over the edge of a smooth table,” Am. J. Phys. 50 (6), 536–539 (1982).
J. R. Sanmartin and M. A. Vallejo, “Comment on “Another look at the uniform rope sliding over the edge of a smooth table”,” Am. J. Phys. 51 (7), 585 (1983).
M. G. Calcin, “The dynamics of a falling chain: II,” Am. J. Phys. 57 (2), 157–159 (1989).
P. T. Brun, B. Audoly, A. Goriely, and D. Vella, “The surprising dynamics of a chain on a pulley: lift off and snapping,” Proc. R. Soc. London, Ser. A 472, 20160187 (2016).
J. Vrbik, “Chain sliding off a table,” Am. J. Phys. 61 (3), 258–261 (1993).
R. Moreno, A. Page, J. Riera, and J. L. Hueso, “Video analysis of sliding chains: a dynamic model based on variable-mass systems,” Am. J. Phys. 83 (6), 258–261 (2015).
E. G. Virga, “Chain paradoxes,” Proc. R. Soc. London, Ser. A 471, 20140657 (2014).
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Sumbatov, A.S. Plane-Parallel Sliding of a Flexible Inextensible Chain over the Rounded Edge of a Horizontal Table. Mech. Solids 56, 1569–1577 (2021). https://doi.org/10.3103/S0025654421080173
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DOI: https://doi.org/10.3103/S0025654421080173