Involutes of fronts in the Euclidean plane
Involutes of fronts in the Euclidean plane
复制标题
DOI：
10.1007/s13366-015-0275-1
复制
发表时间：
2012-12
期刊：
影响因子：
--
通讯作者：
Tomonori Fukunaga;Masatomo Takahashi
中科院分区：
文献类型：
--
作者：
Tomonori Fukunaga;Masatomo Takahashi
对于一条规则的平面曲线，它的渐开线是由从曲线的一点展开的拉伸弦的末端所描述的轨迹。即使是规则曲线，渐开线也总是有奇点。利用单位切丛中Legendre浸入的曲率和沿波前沿着的活动标架，定义了欧氏平面中波前的渐开线，并给出了它的性质，同时考虑了无拐点波前的渐屈线与渐屈线之间的关系.结果表明，没有拐点的锋面的渐屈线和渐屈线对应于勒让德浸入曲率的微分和积分。
For a regular plane curve, an involute of it is the trajectory described by the end of a stretched string unwinding from a point of the curve. Even for a regular curve, the involute always has a singularity. By using a moving frame along the front and the curvature of the Legendre immersion in the unit tangent bundle, we define an involute of the front in the Euclidean plane and give properties of it. We also consider a relationship between evolutes and involutes of fronts without inflection points. As a result, the evolutes and the involutes of fronts without inflection points are corresponding to the differential and the integral of the curvature of the Legendre immersion.