力学与实践 ›› 2017, Vol. 39 ›› Issue (4): 359-364.DOI: 10.6052/1000-0879-17-102

• 应用研究 • 上一篇    下一篇

抛物线壁内细杆的摩擦平衡分析

尤明庆   

  1. 河南理工大学能源科学与工程学院, 河南焦作 454010
  • 收稿日期:2017-03-27 修回日期:2017-05-19 出版日期:2017-08-15 发布日期:2017-08-10
  • 通讯作者: 尤明庆,E-mail:youmq@hpu.edu.cn

STABLE EQUILIBRIUM OF A POLE ON A FRICTIONAL PARABOLA WALL

YOU Mingqing   

  1. School of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo, 454010, China
  • Received:2017-03-27 Revised:2017-05-19 Online:2017-08-15 Published:2017-08-10

摘要:

细杆在抛物线壁内支承,平衡特性与杆长、倾角和摩擦因子相关.细杆在自身重力作用下可发生焦点下方的顺时针运动,焦点上方的逆时针运动以及两端同时下滑.基于端部支撑力达到摩擦锥边界的条件,可确定细杆状态为不平衡、稳定或不稳定的平衡和摩擦平衡.平衡集为具有宽度的叉式分岔.

关键词:

抛物线|细杆|摩擦|稳定平衡|分岔

Abstract:

The equilibrium of a pole supported on a parabola wall is related to its length, slope angle and the frictional factor between them. Under the action of gravity, the pole can move clockwise under the focus of parabola, and move counterclockwise or slide down at two ends over the focus. The state of pole, i.e. disequilibrium, stable and unstable equilibrium with friction, is determined on the support force at the boundary of friction cone. The equilibrium set is a pitchfork bifurcation with width related to the frictional factor.

Key words:

parabola wall|pole|friction|stable equilibrium|bifurcation

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