论文标题
不中心气缸的腕骨
Brachistochrone of off-centered cylinders
论文作者
论文摘要
我们考虑在两个点之间找到最短的过境时间的问题（通常称为Brachistochrone），该圆柱体的质量不偏置，不带滑动滚动，仅受重力的作用。使用经典刚体动力学的原理设置此问题，并且使用变异的离散计算方法来求解所需的路径函数。我们发现了针对不中心的圆柱体的一系列不同的腕骨轨迹轨迹，这表明了这种路径对质量质量的初始位置和方向的关键依赖性，并将新的见解带入了腕足激素问题和解决方案的家族。
We consider the problem of finding paths of shortest transit time between two points (popularly known as Brachistochrone) for cylinders with off-centered center of mass, rolling down without slip, subject solely to the force of gravity. This problem is set up using principles of classical rigid body dynamics and the desired path function is solved for numerically using the method of discrete calculus of variations. We discover a distinct array of brachistochrone trajectories for off-centered cylinders, demonstrate a critical dependence of such paths on the initial location and orientation of cylinders' centers of mass and bring new insights into the family of brachistochrone problems and solutions.
