pursuitrotor

Pursuit rotor is a theoretical model used in mathematics and control theory to study pursuit dynamics. It describes a pursuer moving at a fixed speed that is always directed toward a target whose motion is prescribed. The model abstracts a pursuit scenario in which the pursuer’s velocity vector at any moment points along the line from the pursuer to the target, rather than toward a fixed destination.

In typical formulations, the target follows a known path, such as a straight line or a circle, while the pursuer maintains a constant speed. The resulting trajectory of the pursuer is governed by a set of nonlinear differential equations, often leading to pursuit curves. When the target moves along a circular path with constant speed, the pursuer’s path frequently takes the form of a logarithmic spiral that winds toward the target’s trajectory. The qualitative behavior of the pursuit depends on the relative speeds of the two agents and the chosen target path; different speed ratios can yield capture, endless pursuit, or convergence to a limiting orbit.

The pursuit rotor model serves as a simplified framework for exploring concepts in differential equations, geometry, and control strategies. It is used in teaching to illustrate how simple local rules (always aiming at the target) can generate complex global trajectories, and it informs discussions in robotic guidance, autonomous systems, and pursuit–evasion research.

See also pursuit curve, pursuit–evasion, geometric control.