球坐标系中加速度形式的几何求法

Geometric Solution of Acceleration Form in Spherical Coordinate System

球坐标系中加速度的推导是理论力学教学中的一个难点,然而目前常用的推导方法都过于抽象,不容易被学生理解和掌握。利用极限思想和运动合成与分解的思想通过几何方法同样可以推导出球坐标系的加速度形式,而且该推导过程比已有方法更加直观,易于理解,有利于培养学生的空间想象力,还可用于大学物理和高中物理教学当中。

The derivation of the particle acceleration in spherical coordinates is a difficult point in the teaching of theoretical mechanics. However, the commonly used derivation methods at present are too abstract to be easily understood and mastered by students. Using the limit thought and the idea of motion synthesis and decomposition, the form of the particle acceleration in spherical coordinates can also be deduced by a geometric method. Moreover, the derivation process is more intuitive and easy to understand than the existing methods, is beneficial to cultivate the spatial imagination of students, and can be introduced into the physics teaching of colleges and hiKgh schools.