 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| << Previous article | Volume 47, Issue 4 / 2012 | Next article >> |
| 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 |
| Link to Fulltext |
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