Galileo was the first to analyze the motion of spheres rolling down an inclined surface. Since then, Coulomb’s law of dry friction has covered the case of sliding particles. However, a particle that is not round can still roll, although in a way that is essentially different from the motion studied by Galileo. Instead of keeping contact with the surface, such particles will start bouncing after reaching a certain angular velocity. This motion is a combination of flying and colliding. It is shown that the acceleration of a bouncing particle is always bounded by the accelerations for perfect rolling and sliding. In order to describe the motion of a not perfectly round particle, the polygon is used as a model. The aim of the model is to predict the trajectories of particles that cannot be covered by the models for perfect rolling and sliding.
The Motion of a Rolling Polygon
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, December 12, 1999; final revision, December 21, 2001. Associate Editor: A. A. Ferri. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
- Views Icon Views
- Share Icon Share
- Cite Icon Cite
- Search Site
Beunder, E. M., and Rem, P. C. (March 27, 2003). "The Motion of a Rolling Polygon ." ASME. J. Appl. Mech. March 2003; 70(2): 275–280. https://doi.org/10.1115/1.1481893
Download citation file:
- Ris (Zotero)
- Reference Manager