›› 2015, Vol. 34 ›› Issue (8): 16-16.

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  1. 东阿县第一中学,山东东阿252201
  • 出版日期:2015-08-25 发布日期:2015-08-20

Proving of branchistochrone and isochronous artfully

  • Online:2015-08-25 Published:2015-08-20

摘要: 分析摆线形成的物理过程,写出参数方程,根据速度的合成规律求出摆线上各点的切线方向和摆线的长度,类比费马原理以及简谐运动与圆周运动的等效性,求证摆线的"最速性"和"等时性".

关键词: 摆线, 最速降线, 等时曲线

Abstract: The physical process of the formation of a cycloid is analyzed and the parameter equation is obtained. According to the law of vector for the velocity,the direction of tangent of each point of the cycloid and the length of the cycloid are calculated. An analogy on the Fermat's theory and the equivalence of simple harmonic motion and circular motion are made and thus the fastest falling line and "isochronous"of the cycloid are proved.

Key words: cycloid, brachistochrone, tautochrone


  • O313.1