一般旋转曲面方程研究  

Study on the equation of general rotating surface

作　　者：丁尚文 DING Shangwen(Foundation Department of Xuancheng Campus,Hefei University of Technology,Xuancheng 242000,Anhui Province,China)

机构地区：[1]合肥工业大学宣城校区基础部,安徽宣城242000

出　　处：《浙江大学学报（理学版）》2022年第6期651-656,681,共7页Journal of Zhejiang University（Science Edition）

基　　金：安徽省2020年省级教学质量与教学改革工程项目(2020jyxm1486)。

摘　　要：旋转曲面方程是高等数学中向量代数与空间解析几何教学的重点内容之一。现有的高等数学教材较多涉及与坐标轴共面的曲线绕坐标轴旋转所成的曲面方程求解问题。以坐标平面上曲线绕坐标轴旋转所成的旋转曲面方程为基础,通过寻找2个坐标系之间的姿态和相对位置,利用方向角和转轴公式推导了空间曲线绕定直线旋转所成的一般旋转曲面方程。提出的一般旋转曲面方程求解方法是对旋转曲面方程教学内容的有益补充,具有一定的参考价值。The equation of rotating surface is one of the key contents in the teaching of vector algebra and spatial analytic geometry in higher mathematics. The existing higher mathematics textbooks mostly concern the solution methods of the surface equation formed by the rotation of the coplanar curve on the coordinate plane around the coordinate axis. Based on the equation of the such rotating surfaces, this paper deduces the equation of the general rotating surface formed by rotating a space curve around a fixed space line by using the formula of direction angle and rotation axis. It determines the rotation axis by looking for attitude and its relative position between the two coordinate systems. The method for solving the general equation of rotating surface proposed in this paper not only is a useful supplement to the current teaching content, but also provides a practical reference for constructing the surface rotation.

关 键 词：旋转曲面 转轴公式 方向角 方向余弦 

分 类 号：O13[理学—数学]