大学物理 ›› 2016, Vol. 35 ›› Issue (8): 25-28.

• 编者按 • 上一篇    下一篇

力学问题和光学问题的关联:由悬链线和海市蜃楼说起

赵虎,王棋   

  1. 北京师范大学物理学系,北京100875
  • 收稿日期:2015-11-18 修回日期:2016-01-04 出版日期:2016-08-20 发布日期:2016-08-20
  • 作者简介:赵虎( 1969—) ,男,河北景县人,北京师范大学物理系副教授,博士,主要从事基础物理教学和多体理

The connections between optical and mechanical problems: by talking about catenary and mirage

ZHAO Hu,WANG Qi   

  1. Department of Physics,Beijing Normal University,Beijing 100875,China
  • Received:2015-11-18 Revised:2016-01-04 Online:2016-08-20 Published:2016-08-20

摘要: 首先简要介绍了悬链线和海市蜃楼问题的数学模型和传统解法,随后讨论了如何利用折射定律求解悬链线方程和利用拉氏量来描述海市蜃楼的形成.在分析二者之间的数学模型相关联的基础上,重新强调了在大学物理教学中重视哈密顿原理与费马原理之间密切联系的必要性.

关键词: 悬链线, 哈密顿原理, 海市蜃楼, 费马原理

Abstract: The mathematical model and conventional solution of catenary and mirage are briefly introduced at first. Then, the catenary equation is discussed in terms of Snell’s Law, and the forming of a mirage is described on the basis of Lagrangian. Based on the analysis of the relations between these two mathematical models, the value of the connections between Hamilton’s principle and Fermat’s principle is re-emphasized for the physics education at university.

Key words: Hamilton principle, mirage, Fermat s principle