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IssuesArchive of Issues2012-4pp.380-384

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V.P. Legeza, "Cycloidal Pendulum with a Rolling Cylinder," Mech. Solids. 47 (4), 380-384 (2012)
Year 2012 Volume 47 Number 4 Pages 380-384
DOI 10.3103/S0025654412040024
Title Cycloidal Pendulum with a Rolling Cylinder
Author(s) V.P. Legeza (National University of Food Technologies, Vladimirskaya†68, Kiev, 01601 Ukraine, viktor.legeza@gmail.com)
Abstract Free vibrations of a heavy homogeneous cylinder rolling in a cylindrical cavity whose directing curve is a brachistochrone are considered. The equation of motion of the cylinder is derived and the circular frequency of free vibrations of the cylinder center of mass is determined. An analogy between the cycloidal pendulum with a rolling cylinder and the classical cycloidal pendulum in the form of a material point is obtained.
Keywords brachistochrone for a cylinder, cycloidal pendulum, isochronous vibrations, slip-free rolling
References
1.  V. P. Legeza, Vibroprotection of Dynamical Systems by Roller Dampers (Chetverta Khvilya, Kiev, 2010) [in Ukrainian].
2.  V. P. Legeza, "Quickest-Descent Curve in the Problem of Rolling of a Homogeneous Cylinder," Prikl. Mekh. 44 (12), 131-138 (2008) [Int. Appl. Mech. (Engl. Transl.) 44 (12), 1430-1436 (2008)].
3.  V. P. Legeza, "Brachistochrone for a Rolling Cylinder," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 34-41 (2010) [Mech. Solids (Engl. Transl.) 45 (1), 27-33 (2010)].
4.  L. D. Akulenko, "An Analog of the Classical Brachistochrone for a Disk," Dokl. Ross. Akad. Nauk 419 (2), 193-196 (2008) [Dokl. Phys. (Engl. Transl.) 53 (3), 156-159 (2008)].
5.  L. D. Akulenko, "The Brachistochrone Problem for a Disc," Prikl. Mat. Mekh. 73 (4), 520-530 (2009) [J. Appl. Math. Mech. (Engl. Transl.) 73 (4), 371-378 (2009)].
6.  E. Rogers, "Brachistochrone and Tautochrone Curves for Rolling Body," Am. J. Phys. 14 (4), 249-242 (1964).
7.  K. Magnus, Vibrations. Introduction to the Study of Oscillatory Systems (Mir, Moscow, 1982) [in Russian].
Received 29 January 2010
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