Relative Equilibria of a Heavy Point on a Uniformly Rotating Inclined Plane-Reference-Cited by-同舟云学术

Relative Equilibria of a Heavy Point on a Uniformly Rotating Inclined Plane

Published:2023-01-01 Issue:1 Volume: Page:156-165
ISSN:1026-3519
Container-title:Известия Российской академии наук. Механика твердого тела
language:
Short-container-title:Izvestiâ Rossijskoj akademii nauk. Mehanika tverdogo tela

Author:

Burov A. A.¹,Nikonov V. I.¹

Affiliation:

1. Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences

Abstract

The problem of the motion of a heavy point along an inclined plane that rotates uniformly around the vertical is considered. The area filled with non-isolated relative equilibria is determined, its dependence on the parameters of the problem - the angular velocity, the angle of inclination of the plane and the angle of friction - is studied. The stability of the studied relative equilibria is discussed.

Publisher

The Russian Academy of Sciences

Reference25 articles.

1. Burov A.A. On bifurcations of relative equilibria of a heavy bead sliding with dry friction on a rotating circle // Acta Mech. 2010. V. 212. № 3–4. P. 349–354. https://doi.org/10.1007/s00707-009-0265-1

2. Burov A.A., Shalimova E.S. On the motion of a heavy material point on a rotating sphere (dry friction case) // Regular Chaotic Dyn. 2015. V. 20. № 3. P. 225–233. https://doi.org/10.1134/S1560354715030028

3. Буров А.А., Шалимова Е.С. Бифуркация относительных равновесий тяжелой бусинки на вращающейся параболоидальной чаше с сухим трением // Изв. РАН. Механика твердого тела. 2016. № 4. С. 30–42.

4. Иванов А.П. Об устойчивости равновесия в системах с трением // ПММ. 2007. Т. 71. № 3. С. 427–438.

5. Иванов А.П. Бифуркации в системах с трением: основные модели и методы // Нелинейная динамика. 2009. Т. 5. № 4. С. 479–498. https://doi.org/10.20537/nd0904003