摘要
研究介绍了一种将质点在极坐标系的动能对矢径求导来求有心力的方法,称动能导数法。应用该方法求出做圆锥曲线运动的质点所受的有心引力,继而求出质点的势能函数和守恒的总能量。而将动能表示成矢径的函数及角动量守恒是上述推理的前提。经与比耐公式法相比较,发现动能导数法的推理过程更简洁,其所推得的诸能量的物理意义也更清楚。总能量的表达式是研究的另一个重要的结论,它具有普适性,具体的推理思路、结论或可为相关内容的教学提供一些参考。
This paper introduces a method of finding central force by derivative of the kinetic energy of a particle in a polar coordinate system to the radius vector, called the kinetic energy derivative method. The central gravity acting on a moving particle in a conic curve is obtained by this method, and then the potential energy function and the conserved total energy of the particle are obtained in this paper. The function of kinetic energy expressed as radius vector and the conservation of angular momentum are the premises of the above reasoning. Compared with Binet′s formula method, it is found that the reasoning process of kinetic energy derivative method is simpler and the physical meaning of the energy derived is clearer. The expression of total energy is another important conclusion of this paper, which has universal applicability. The reasoning ideas and conclusions of the article may provide some reference for the teaching of related content.
作者
邵云
SHAO Yun(School of Electronic Engineering,Nanjing Xiaozhuang University,Nanjing Jiangsu 211171)
出处
《巢湖学院学报》
2019年第6期75-79,共5页
Journal of Chaohu University
基金
南京晓庄学院优秀教学团队建设项目(项目编号:4187061)
关键词
圆锥曲线
有心力
动能导数法
比耐公式
优点
conic curve
centrifugal force
kinetic energy derivative method
Binet′s formula
advantage
