大学物理 ›› 2017, Vol. 36 ›› Issue (10): 24-28.doi: 10. 16854 /j. cnki. 1000-0712. 2017. 10. 008

• 教学讨论 • 上一篇    下一篇

"绳连三球”系统运动的轨迹方程和周期的研究

郎军,姜付锦   

  1. 1. 重庆市第十一中学校,重庆400061; 2. 武汉市黄陂区第一中学,湖北武汉430300
  • 出版日期:2017-10-20 发布日期:2017-10-20
  • 作者简介:郎军( 1970—) ,男,重庆万州人,重庆市第十一中学校物理高级教师,理学学士,主要从事高中物理教学和物理竞赛辅导工作.

Research on the trajectory equation and the cycle of the system of one rope with three balls

 LANG Jun,JIANG Fu-jin   

  1. 1. Chongqing NO. 11 Middle School,Chongqing 400061,China; 2. Wuhan Huangpi NO. 1 Middle School,Wuhan,Hubei 430300,China
  • Online:2017-10-20 Published:2017-10-20

摘要: 对于光滑水平面上由“绳连三球”构成的系统,利用参数方程分别对其运动轨迹和周期进行了研究,发现子球运动 轨迹与绳子的长度和质量比有关,系统运动的周期与绳子的长度、质量比及初速度有关,利用软件模拟出子球运动轨迹、速度相图和速度时间图象.

关键词: 绳连三球, 轨迹, 周期, 第二类椭圆积分

Abstract: For a system composed of one rope with three balls on a sooth horizontal plane,its trajectory and cycle are studied by using parametric equations. It is indicated that the ball's trajectory is related to the length of the rope and the ratio of mass,as well as the cycle of the system is connected with the length of the rope,mass ratio,and initial speed. The ball's trajectory, the phase diagram of speed and velocity graph are simulated by using software.

Key words: one rope with three balls, trajectory, cycle, elliptic integral of the second kind