两种坐标系下速度(率)、能量、动量的分布

Velocity, Energy and Momentum’s Distribution Based on Two Coordinate System

摘要: 本文以速度的分布为基础，推导出了在直角坐标系和球坐标系下能量和动量的分布，并计算出在两种坐标系下的最概然速率和最概然能量、平均速度、平均能量和平均动量等相关物理量。通过对计算结果的分析我们发现：在两类坐标系下，标量的计算结果是一致的，矢量的计算结果是不同的。本文还介绍了麦克斯韦分布的适用范围，以及麦克斯韦能量分布的最概然能量对应的速率与麦克斯韦速率分布的最概然速率数值不相等的原因。

Abstract: In this paper, the distribution of velocity in Cartesian coordinates and spherical coordinates de-duces on the basis of the distribution of energy and momentum, and calculates the most probable speed in both coordinates and the most probable energy, average speed, average energy and av-erage momentum and other related physical quantities. Through the analysis results, we found that: in the both coordinates, the calculation result was consistent with scalar, vector calculation results were different. This paper also studied the scope of Maxwell distribution and the reason why the most probable energy Maxwell energy distribution corresponding speed and the most probable speed of Maxwell velocity distribution values were not equal.