基于3D打印与轨迹追踪探究最速降线问题

Exploring the Brachistochrone Problem Based on 3D Printing and Trajectory Tracking

采用SolidWorks软件建立最速降线轨道模型,通过3D打印技术获得最速降线教具.再通过轨迹追踪软件Tracker分析实验过程中的轨迹、加速度随时间变化的关系,分析图像发现加速度随时间的增加而减小,并探究了从不同高度下落的物体运动的时间,证明了物体从最速降线的不同位置下落具有等时性.

SolidWorks software was used to establish the brachistochrone curve model,and the brachistochrone curve teaching aid was obtained through 3D printing technology.The relationship between trajectory and acceleration with time during the experiment was analyzed by Tracker software,and the images were analyzed to find that the acceleration decreased with the increase of time.And the time of motion of objects falling from different heights was investigated,which proved that the objects falling from different positions along the most rapid descent line had isochronism.