Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

On detachment conditions in the problem on the motion of a rigid body on a rough plane

On detachment conditions in the problem on the motion of a rigid body on a rough plane The classical mechanical problem about the motion of a heavy rigid body on a horizontal plane is considered within the framework of theory of systems with unilateral constraints. Under general assumptions about the character of friction, we examine the question on the possibility of detachment of the body from the plane under the action of reaction of the plane and forces of inertia. For systems with rolling, we find new scenarios of the appearing of motions with jumps and impacts. The results obtained are applied to the study of stationary motions of a disk. We have showed the following. 1) In the absence of friction, the detachment conditions on stationary motions do not hold. However, if the angle θ between the symmetry axis and the vertical decreases to zero, motions close to stationary motions are necessarily accompanied by detachments. 2) The same conclusion holds for a thin disk that rolls on the support without sliding. 3) For a disk of nonzero thickness in the absence of sliding, the detachment conditions hold on stationary motions in some domain in the space of parameters; in this case, the angle θ is not less than 49 degrees. For small values of θ, the contact between the body and the support does not break in a neighborhood of stationary motions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

On detachment conditions in the problem on the motion of a rigid body on a rough plane

Regular and Chaotic Dynamics , Volume 13 (4) – Aug 31, 2008

Loading next page...
 
/lp/springer-journals/on-detachment-conditions-in-the-problem-on-the-motion-of-a-rigid-body-8r4UnrREg8

References (24)

Publisher
Springer Journals
Copyright
Copyright © 2008 by MAIK Nauka
Subject
Mathematics; Dynamical Systems and Ergodic Theory
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354708040096
Publisher site
See Article on Publisher Site

Abstract

The classical mechanical problem about the motion of a heavy rigid body on a horizontal plane is considered within the framework of theory of systems with unilateral constraints. Under general assumptions about the character of friction, we examine the question on the possibility of detachment of the body from the plane under the action of reaction of the plane and forces of inertia. For systems with rolling, we find new scenarios of the appearing of motions with jumps and impacts. The results obtained are applied to the study of stationary motions of a disk. We have showed the following. 1) In the absence of friction, the detachment conditions on stationary motions do not hold. However, if the angle θ between the symmetry axis and the vertical decreases to zero, motions close to stationary motions are necessarily accompanied by detachments. 2) The same conclusion holds for a thin disk that rolls on the support without sliding. 3) For a disk of nonzero thickness in the absence of sliding, the detachment conditions hold on stationary motions in some domain in the space of parameters; in this case, the angle θ is not less than 49 degrees. For small values of θ, the contact between the body and the support does not break in a neighborhood of stationary motions.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Aug 31, 2008

There are no references for this article.