Pursuit Problem with an Arbitrary Initial Aiming Angle

An exact solution to the pursuit problem in the predator-prey system is obtained for an arbitrary initial aiming angle of  0° < α₀ < 180° in the form of an equation of the pursuit curve. Exact implicit time equations for the motion of the predator and prey and the distance between them are obtained. The lengths of the pursuit curves are found for arbitrary angles α₀, including the shortest pursuit curve. A realistic numerical simulation of the movement of the predator and prey in space and time has been carried out. The area of a successful pursuit with a limited resource for the movement of the predator is determined. The obtained general solution of the pursuit problem with an arbitrary initial aiming angle provides broad-ranging opportunities for numerical modeling, which is important for providing a high level of applied mathematical training for future researchers, engineers, and teachers.