Please wait a minute...
浙江大学学报(理学版)  2022, Vol. 49 Issue (6): 651-656    DOI: 10.3785/j.issn.1008-9497.2022.06.001
数学与计算机科学     
一般旋转曲面方程研究
丁尚文()
合肥工业大学 宣城校区基础部,安徽 宣城 242000
Study on the equation of general rotating surface
Shangwen DING()
 全文: PDF(1156 KB)   HTML( 16 )
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。

关键词: 旋转曲面转轴公式方向角方向余弦    
Abstract:

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.

Key words: rotating surface    shaft formula    direction angle    directional cosin
收稿日期: 2022-03-01 出版日期: 2022-11-23
CLC:  O 13  
基金资助: 安徽省2020年省级教学质量与教学改革工程项目(2020jyxm1486)
作者简介: 丁尚文(1981—),ORCID: https: //orcid.org/0000-0001-5956-3324,男,博士,讲师,主要从事大学数学课程与教学研究,E-mail:dshou1@126.com.
服务  
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章  
丁尚文

引用本文:

丁尚文. 一般旋转曲面方程研究[J]. 浙江大学学报(理学版), 2022, 49(6): 651-656.

Shangwen DING. Study on the equation of general rotating surface. Journal of Zhejiang University (Science Edition), 2022, 49(6): 651-656.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2022.06.001        https://www.zjujournals.com/sci/CN/Y2022/V49/I6/651

图1  平面曲线C绕z轴旋转
图2  空间曲线Γ绕z'轴旋转
图3  空间曲线Γ绕z'轴旋转
图4  空间曲线Γ绕z'轴旋转
图5  空间曲线Γ绕z'轴旋转
1 朱士信, 唐烁. 高等数学(下册)[M]. 北京:高等教育出版社, 2020.
ZHU S X, TANG S. Advanced Mathematics (Volume Ⅱ)[M]. Beijing: Higher Education Press, 2020.
2 同济大学数学系 .高等数学(下册)[M].北京:高等教育出版社,2019.
Department of Mathematics, Tongji University. Advanced Mathematics(Volume Ⅱ)[M]. Beijing: Higher Education Press, 2019.
3 黄振华,祝秋文,胡清华.旋转曲面及其方程[J].湖北师范大学学报(自然科学版),2017,37(2):83-86.
HUANG Z H, ZHU Q W, HU Q H. Rotation surface equation[J]. Journal of Hubei University (Natural Science),2017, 37(2):83-86.
4 谭畅,曲智林. 关于旋转曲面方程的注记[J]. 大学数学, 2020,36(5):101-105. doi:10.3969/j.issn.1672-1454.2020.05.017
TAN C, QU Z L. A note on the equation of rotating surface[J]. College Mathematics, 2020,36(5): 101-105. doi:10.3969/j.issn.1672-1454.2020.05.017
doi: 10.3969/j.issn.1672-1454.2020.05.017
5 张树功,雷娜,刘停战.计算机代数基础:代数与符号计算的基本原理[M]. 北京:科学出版社,2005:44-50.
ZHANG S G, LEI N, LIU T Z. Fundamentals of Computer Algebra: Basic Principles of Algebra and Symbolic Computing[M]. Beijing: Science Press, 2005:44-50.
6 刘绍学, 朱元森. 数学辞海[M].北京:中国科学技术出版社, 2002:85-95.
LIU S X, ZHU Y S. Mathematical Lexicon[M]. Beijing: China Science and Technology Press, 2002:85-95.
No related articles found!