论文标题
机械斯内尔定律
Mechanical Snell's Law
论文作者
论文摘要
我们研究了一个巨大的粒子的运动，这些粒子约束以沿着由任意保守力下的垂直平面上的两个线段组成的路径移动。通过固定轨道的起点和终点并水平改变顶点，我们找到了最小的路径。我们定义了类似于光线的折射的入射和折射角度。值得注意的是，只要保守力的水平分量消失，这些角度的罪恶之比与两部分路径上平均速度的比率相同。
We investigate the motion of a massive particle constrained to move along a path consisting of two line segments on a vertical plane under an arbitrary conservative force. By fixing the starting and end points of the track and varying the vertex horizontally, we find the least-time path. We define the angles of incidence and refraction similar to the refraction of a light ray. It is remarkable that the ratio of the sines of these angles is identical to the ratio of the average speeds on the two partial paths as long as the horizontal component of the conservative force vanishes.
