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A dynamic path-planning algorithm is proposed for routing unmanned air vehicles (UAVs) in order to track ground targets under path constraints, wind effects, and obstacle avoidance requirements. We first present the tangent vector field guidance (TVFG) and the Lyapunov vector field guidance (LVFG) algorithms. We demonstrate that the TVFG outperforms the LVFG as long as a tangent line is available between the UAV's turning circle and an objective circle, which is a desired orbit pattern over a target. Based on a hybrid version of the TVFG and LVFG, we then derive a theoretically shortest path algorithm with UAV operational constraints given a target position and the current UAV dynamic state. This algorithm has the efficiency of the TVFG when UAV is outside the standoff circle and the ability to follow the path via the LVFG when inside the standoff circle. In addition we adopt point-mass approximation of the target state probability density function (pdf) for target motion prediction by exploiting road network information and target dynamics as well as obstacle avoidance strategies. Overall, the proposed technical approach is practical and competitive, supported by solid theoretical analysis on several aspects of the algorithm performance. With extensive simulations we show that the tangent-plus-Lyapunov vector field guidance (T+LVFG) algorithm provides effective and robust tracking performance in various scenarios, including a target moving according to waypoints or a random kinematics model in an environment that may include obstacles and/or winds.