论文标题
光线和欧拉的倾斜角度的苛刻
Caustics of light rays and Euler's angle of inclination
论文作者
论文摘要
Euler使用了表达曲率半径作为倾斜角度的固有方程，以找到类似于其进化的曲线。我们从光学上解释了平面曲线的进化，为正常光线的腐蚀性（包膜），并研究了欧拉（Euler）的一般苛刻问题。当射线与曲线保持恒定角度时，表征所得的曲线，从而推广了Evolutes的情况。除了经典解决方案的类似物外，我们遇到了一些新类型的曲线。我们还考虑了曲面反射反射的平行射线的苛性射线，在该镜像中，Euler的问题导致了新型的全能力仪方程，并描述了其分析解决方案。
Euler used intrinsic equations expressing the radius of curvature as a function of the angle of inclination to find curves similar to their evolutes. We interpret the evolute of a plane curve optically, as the caustic (envelope) of light rays normal to it, and study the Euler's problem for general caustics. The resulting curves are characterized when the rays are at a constant angle to the curve, generalizing the case of evolutes. Aside from analogs of classical solutions we encounter some new types of curves. We also consider caustics of parallel rays reflected by a curved mirror, where Euler's problem leads to a novel pantograph equation, and describe its analytic solutions.
