如果在斜面上释放一个双接触点旋转对称的刚体，例如螺栓，当超过一定临界条件时会表现出有趣的非线性现象，即刚体在垂直于斜面方向的扭转幅度会逐渐增大；当不满足此临界条件时，螺栓振荡幅度会逐渐减小. 在两接触点处，刚体相对斜面只能滑动或滚动，根据两点滑动或滚动，能组合出四种模式. 每种模式下的运动约束和受力情况各不相同，用于数值计算的动力学微分方程也不同. 使用MATLAB进行数值仿真，编写数值计算程序，动态计算滑动和滚动状态之间的临界点，来控制程序切换到相应模式进行求解. 通过在一定范围内遍历计算初始参数，确定了释放时决定摆幅增大或减小的临界点，这一临界点与斜坡倾角、螺丝半顶角和初始释放角度有关. 对临界点数据采用二次曲面拟合的方式，得到临界点满足的经验函数，并进行了相关实验，实验结果与计算结果符合良好. 该研究可以作为一个教学案例，用来演示如何使用数值计算软件探究双接触点旋转对称刚体在干摩擦情况下的滑动-滚动转换.

A bolt-shaped object released from an inclined plane at rest could exhibit intriguing nonlinear phenomena, wherein the twist or rotation amplitude of a rigid body perpendicular to the inclined plane increases upon surpassing a critical condition. When such a rigid body is in contact with two rigid surfaces at two points in the presence of dry friction, four motion modes occur due to the rolling or slipping state at each contact point. The constraints and forces under each mode differ, leading to differences in the dynamical equations. A MATLAB program dynamically switches to the corresponding mode based on the conditions between slipping and rolling states for numerical calculations. By exploring the initial parameters within a certain range, we identify the critical points that determine the increase or decrease of amplitude during release. These critical points correlate with the inclination angle of the inclined plane, semiapex angle of the bolt, and the twist angle at initial release. We utilize a quadric surface to fit the critical points and derive the empirical function of the critical condition. The experimental results demonstrate good agreement with theoretical calculations. This example involving a bolt serves as a practical case study for teaching the analysis of slipping-rolling transitions of a rigid body under two-point contact constraints on a plane in the presence of dry friction using numerical methods.