Sphere rolling on the surface of a cone
Classical Physics
2009-11-11 v1
Abstract
We analyse the motion of a sphere that rolls without slipping on a conical surface having its axis in the direction of the constant gravitational field of the Earth. This nonholonomic system admits a solution in terms of quadratures. We exhibit that the only circular of the system orbit is stable and furthermore show that all its solutions can be found using an analogy with central force problems. We also discuss the case of motion with no gravitational field, that is, of motion on a freely falling cone.
Keywords
Cite
@article{arxiv.physics/0602160,
title = {Sphere rolling on the surface of a cone},
author = {I Campos and J L Fernández-Chapou and A L Salas-Brito and C A Vargas},
journal= {arXiv preprint arXiv:physics/0602160},
year = {2009}
}
Comments
12 pages, 2 figures, to be published in Eur J Phys