The dynamics of a constrained three-vortex system, a pair of point vortices of arbitrary non-zero circulations in the velocity field of a fixed point vortex, is investigated. The underlying dynamical system is simplified using a coordinate transformation and categorized into two cases based on the zero and non-zero values of the constant of angular impulse. For each case, dynamical features of the vortex motion are studied analytically in the transformed plane to completely classify the vortex motions and understand the boundedness and periodicity of the inter-vortex distances. The theoretical predictions are also verified numerically and illustrated for various sets of initial conditions and circulations.

研究了约束三涡系统的动力学，即固定点涡的速度场中任意非零环流的一对点涡。底层动力系统使用坐标变换进行简化，并根据角脉冲常数的零值和非零值分为两种情况。对于每种情况，在变换平面中分析研究涡旋运动的动力学特征，以完全分类涡旋运动并了解涡旋间距离的有界性和周期性。理论预测也得到了数值验证，并针对各种初始条件和循环进行了说明。