研究一种绳约束下两质点运动的动力学模型和运动规律，分别采用泰勒级数展开的方法和四阶龙格-库塔数值方法，得到了质点运动微分方程的近似解和数值解.通过对系统的动力学方程计算，给出了位置矢量随时间的演化曲线、运动相图和运动轨迹.研究发现系统的运动与初始位置和速度有关，在初速度较大和较小时，系统作非线性周期性运动.存在临界初始速度，使得系统处于平衡态，在微小扰动下系统在初始位置附近作近似简谐振动.以上研究结果对微小振动力学问题的教学 　　和科研具有一定的参考价值.

The dynamics model and the motion of string-bound two-body particles are studied.By using the Taylor series expansion method and the Runge- Kutta numerical method，the approximate and numerical solution of differential equations are obtained，respectively.Calculations of the dynamic equation give the evolution of position vector as a function of time，motion trajectory and phase diagrams. The motion of particle depends on the initial position and transverse velocity.For a larger or smaller initial transverse velocity，the motion is non-linear oscillation. There is a critical initial velocity at which the two-body system is in mechanical equilibrium，and will perform harmonic vibration under small perturbation.The results are valuable for teaching and research on the mechanics 　　problems of micro-vibrations.