工程结构中圆锥曲线分析与应用

Analysis and Application of Cone Curved Lines in Engineering Construct

目的分析工程结构中圆锥曲面被平面所截得到的圆锥曲线各种特性,为复杂曲面问题的数学化解释和工程应用提供条件与参考.方法基于向量代数,采用空间坐标变换方法,建立了圆锥面与平面相交中截交曲线的形成特点,讨论了二次曲线的构成的数学原理.结果通过空间不同情况下圆锥截交线的坐标变换,获得了圆锥截交线的真实特征.结论应用向量分析的坐标化的数学原理,有效地证明了圆锥被一般位置平面所截所得到截交线为二次曲线.并为解决工程中复杂曲面被平面所截问题的研究提供了思路.

This article aims at analyzing property of cone curved line by mathematical method. Projective transformation of curved surface and plane intersecting line are completed based on vector algebra, adopting space coordinate transforming method. Forming principle of cone quadratic curved line is analyzed and result is given. Typical example of cone curved lines is solved. Applying mathematical principle about vector analysis ,it is proved that intersecting line with cone curved surface and ordinary displace plane is quadratic curved line. The method can be used to deal with complex problem about intersect of curved surface and plane.