Geodesic
Pursuit problem with an arbitrary initial aiming angle
Matematičeskoe modelirovanie, Tome 35 (2023) no. 11, pp. 35-46

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An exact solution to the pursuit problem in the "predator-prey" system is obtained for an arbitrary initial aiming angle $0\alpha_0180^\circ$ in the form of the equation of the pursuit curve. Exact implicit time equations for the motion of predator and prey and the distance between them are obtained. The lengths of the pursuit curves are found for arbitrary angles $\alpha_0$, including the shortest pursuit curve. A realistic numerical simulation of the movement of predator and prey in space and time has been carried out. The area of success of 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 wide opportunities for numerical modeling, which is important for providing a high level of applied mathematical training for future researchers, engineers, and teachers.
Keywords: pursuit problem, mathematical modeling, numerical modeling. 
@article{MM_2023_35_11_a2,
     author = {V. Yu. Bodryakov},
     title = {Pursuit problem with an arbitrary initial aiming angle},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {35--46},
     publisher = {mathdoc},
     volume = {35},
     number = {11},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2023_35_11_a2/}
}
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V. Yu. Bodryakov. Pursuit problem with an arbitrary initial aiming angle. Matematičeskoe modelirovanie, Tome 35 (2023) no. 11, pp. 35-46. http://geodesic.mathdoc.fr/item/MM_2023_35_11_a2/