全部

• 应用研究 • 上一篇    下一篇

水中竖蛋与拉格朗日定理

刘延柱   

  1. 上海交通大学工程力学系, 上海200240
  • 收稿日期:2013-08-19 出版日期:2014-08-08 发布日期:2013-10-16
  • 通讯作者: 刘延柱,教授,主要研究方向为动力学与控制.E-mail:liuyzhc@gmail.com E-mail:liuyzhc@gmail.com

THE ERECTING EGG IN WATER AND LAGRANGE’S THEOREM

LIU Yanzhu   

  • Received:2013-08-19 Online:2014-08-08 Published:2013-10-16

摘要: 鸡蛋在液体中的平衡稳定性问题可作为应用拉格朗日定理判断保守系统稳定性的有趣例子. 分析表明,当液体比重超过某个临界值时,鸡蛋可在液体中实现竖直状态的稳定平衡. 讨论鸡蛋平衡位置数目与稳定性随液体比重变化的静态分岔问题.

关键词: 保守系统|运动稳定性|拉格朗日定理|静态分岔

Abstract: The stability of equilibrium of an egg in liquid is an interesting example of the Lagrange's theorem in determining the stability of conservative system. It is shown that a stable straight equilibrium of an egg in liquid is possible when the specific weight of liquid exceeds a critical value. The static bifurcation problem is discussed that the number and stability of equilibrium attitudes of the egg is variable with the specific weight of liquid.

Key words: conservative system|stability theory|Lagrange’s theorem|static bifurcation

中图分类号: 

  • O317.1