摘要
摆线是重要的平面曲线，它有许多重要性质。摆线、内摆线和外摆线是平面摆线，它们只是球面摆线的特殊情况。本文证明了摆线的三个几何性质对内摆线和外摆线仅部分成立，对球面摆线却一个也不成立。本文还导出了球面摆线的弧长表达式。图４，参３。
Cycloid is an important plane curve. It has a lot of properties,Cycloid,hypocycloid and epicycloid are plane curves .They are only the special examples of ophericslcycloid,This article proves that three geometrical properties of cycloid are partly applied to the hypocycloid and epicycloid, but none of them is applito to the spherical cycloid,The expression of the length of arc for sphentalcydoid is also derived from the article.4figs.,3refs.
出处
《湘潭矿业学院学报》
1994年第2期73-78,共6页
Journal of Xiangtan Mining Institute
关键词
摆线
平面摆线
球面摆线
几何性质
cycloid
planar cycloid
spherical cycloid
geometrical property
