An interesting stability property, as fascinating as that of spinning tops and gyroscopes, is observable in the motion of an unbalanced ring spinning on a rough horizontal surface. An analytical and numerical study is performed to investigate the general motion of an unbalanced ring modeled as a thin ring with a particle attached to its rim. The translational motion is represented by the rectangular coordinates of the ring geometric center. The rotational motion is represented by a 1-2-3 set of Euler angles. The kinetic motion equations are derived with the use of Newton's second law and Euler's rotational motion equations.
The types of motion considered are the pure-rolling and rolling-with-slipping motions. Given favorable initial conditions, ring properties, and a sufficiently large constraint force in the form of friction, the ring undergoes a pure-rolling motion. For other conditions, however, limitations on the magnitude of the friction force render the pure the mathematical model to allow switching from pure-rolling to rolling-with-slipping motion and vice versa.
The general motions of the unbalanced ring, obtained by numerically integrating the governing equations with the use of the seventh-eighth order Runge-Kutta method, are in very good qualitative agreement to those observed during an experiment performed with the use of a high-speed video camera. / Master of Science
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/45606 |
| Date | 10 November 2009 |
| Creators | Budiman, Benny S. |
| Contributors | Engineering Mechanics, Kraige, Luther Glenn, Heller, Robert A., Ragab, Saad A. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis, Text |
| Format | ix, 73 leaves, BTD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 28553018, LD5655.V855_1993.B835.pdf |
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