用矩阵研究一维弹性碰撞与圆周率的关系

Use matrix to study the relationship between one-dimensional elastic collision and PI

采用二阶矩阵高次幂计算一维完全弹性碰撞中多次碰撞后速度的一般表达式,并对碰撞次数分两种情形进行分析,得出实际碰撞总次数与圆周率对应的关系,在此基础上导出用碰撞总次数与两弹性滑块的质量比来近似计算圆周率的表达式及误差估计.

This article uses a second-order matrix n-th power to calculate the general expression of the velocity after the nth collision in a one-dimensional complete elastic collision. From this, the velocity after any collision is obtained. The collision velocity is divided into two cases. Based on the analysis, the corresponding relationship between the actual total number of collisions N and the pi is obtained. On this basis, the expression of the approximate calculation of the pi with the total number of collisions N and the mass ratio k of the two elastic sliders is derived.