双曲狭缝的数学建模分析

Mathematical Modeling Analysis of Hyperbolic Slit

基于对双曲狭缝进行数学建模分析,通过具体数学运算得到了固定屏上投影轨迹的方程.研究发现当屏竖直放置时,斜杆穿过屏的轨迹为双曲线并得到了双曲线方程.通过改变屏与水平面的倾角预言了斜杆穿过屏的轨迹还可以是椭圆和抛物线,而后具体讨论了它们各自的实现条件.

Based on the mathematical modeling analysis of hyperbolic slit,the equation of projection trajectory on the fixed screen is obtained through specific mathematical operations.It is found that when the screen is placed vertically,the trajectory of the oblique bar across the screen is hyperbolic and the hyperbolic equation is obtained.By changing the inclination angle between the screen and the horizontal plane,it is predicted that the trajectory of the inclined rod passing through the screen can also be an ellipse and a parabola.Then the conditions for their realization are discussed concretely.