运用自然坐标系下的运动微分方程，对被约束在抛物线型( 关于x 轴对称) 和椭圆型轨道上的小环运动问题进行了 探究，得到了小环在任意位置处所受约束反作用力( 简称约束反力) 的表达式，并进行了Mathematica 可视化处理，直观地展现 了它的变化规律.研究表明在关于x 轴对称的抛物线型轨道中，小环所受的约束反力是非对称的.两种轨道上的小环所受的约 束反力与轨道参数、小环初始速度以及小环的位置参数有关.我们还讨论了这些参数对约束反力极值点位置的影响，这些结论 可以用于工程设计.

By using the differential equation of motion of natural coordinate system，a moving ringlet is studied， which is restricted on a parabola shaped orbit ( about x axisymmetric) and on an ellipse shaped orbit respectively.The expression of the constraint reaction force of a ringlet is obtained when it moves to any position. Then the solution is visualized by Mathematica software and the variation law of the constraint reaction force is shown intuitively.Research shows that the constraint reaction force of a parabola shaped orbit is asymmetric. Meanwhile，the constraint reaction force of two shaped orbits concerns the parameters of the orbit，the initial velocity，and the position.The influence of these parameters on the position of the extreme point of the constraint reaction force is also discussed. These results can be applied in engineering design.