摘要
分别应用二维曲线曲率半径的直角坐标计算公式和力学矢量计算公式,推导出在极坐标系中曲线曲率半径的一般计算公式;继而应用该公式求出在惯常的极坐标系中圆锥曲线曲率半径的统一表达式,并由此推出在惯常的直角坐标系中诸圆锥曲线各自的曲率半径表达式.文章又利用行星轨道运动的相关动力学结论,直接推导出在惯常的极坐标系中圆锥曲线曲率半径的统一表达式;指出数学与力学推理方法的等价性,以及后者常常更加简便的原因.
In this paper,the general calculation formula of curvature radius of two-dimensional curve in polar coordinate system is derived respectively by using the rectangular coordinate calculation formula and mechanical vector calculation formula of curvature radius of two-dimensional curve.Then the formula is used to get the uniform expression of the curvature radius of the conic in the usual polar coordinate system,according which the expressions of the curvature radius of each conic in the usual rectangular coordinate system are derived.This paper also uses the relevant dynamic conclusions of planetary orbit motion to directly deduce the unified expression of curvature radius of conic curve in the usual polar coordinate system,and points out the equivalence of mathematical and mechanical reasoning methods,as well as the reason why the latter is often more simple.
作者
邵云
窦瑾
SHAO Yun;DOU Jin(School of Electronic Engineering,Nanjing Xiaozhuang College,Nanjing,Jiangsu 211171,China)
出处
《大学物理》
2020年第8期14-17,共4页
College Physics
基金
南京晓庄学院优秀教学团队建设项目(4187061)
江苏省教育科学“十三五”规划课题(D/2020)资助。
关键词
极坐标系
曲线
曲率半径
计算公式
力学
polar coordinate system
curve
curvature radius
calculating formula
mechanics
