雨滴下落运动参量曲线的一种导数判断方法

A derivative judgment method of raindrop falling motion parameter curve

通过求导,可得雨滴动能的一阶导数dE_(k)/dt随速度v的变化函数,结合v~t曲线进行简单的数学分析,便可得dE_(k)/dt大致的变化趋势及Ek~t的变化曲线.此后,若继续对dE_(k)/dt求导,则可得d^(2)E_(k)/dt^(2)随v的变化函数,在数学分析出d^(2)E_(k)/dt^(2)随v或t的变化趋势后,结合v和dE_(k)/dt,便能作出较细致的E_(k)~t变化曲线.于是,a~t曲线便应运而生.这种求导和绘图相结合的分析方法同样适用于其它质点运动情形,及其参量曲线的分析和判断.

The function of the first derivative dE_(k)/dt of raindrop kinetic energy with velocity v can be obtained by derivation.Then,by simple mathematical analysis combining with v~t curve,can get the general change trend of dE_(k)/dt and the general change curve of E_(k)~t.After that,if continue to derive dE_(k)/dt,can get the function of d^(2)E_(k)/dt^(2) with v.After analyzing the changing trend of d^(2)E_(k)/dt^(2) with v or t,combining v and dE_(k)/dt,can draw a more detailed curve of E_(k)~t.Therefore,a~t curve came into being.This method of derivation and drawing is also suitable for the analysis and judgment of other particle motion and other parametric curves.