Pursuit Curve: Vector-Driven Chasing Trajectory

This example demonstrates the pursuit curve that arises when a pursuer always moves in the instantaneous direction of the target in a 2D plane. As time evolves, the relative positions generate a characteristic trajectory that can be analyzed through dynamic behavior. The key mathematical concepts include 2D vectors and directed motion, limiting behavior (convergence/approach in time), similarity transformations (capturing how relative motion scales), and the differential-equation viewpoint implied by the continuous-time update rule for positions and velocities. In GeoGebra, the construction is driven by Textfield-controlled parameters and time controls—objects such as reinicia, empieza, t0, t1, t, tt, dt, tPause, and tPauseAux—to reset and run the animation. Motion is orchestrated with animation-related variables/objects (animation, velocidad, vel, para) and the kinematic elements for both agents, including points/position variables (M, N, P, Q) and their corresponding velocity vectors (vM, vN, velocidad). Text objects (texto1–texto4) are used to present states and guidance. Suitable for advanced high-school learners and early college students studying calculus, vector geometry, parametric motion, and locus/trajectory visualization.