519.17 Pursuit problem in 3D-space with arbitrary initial aiming angles

Bodryakov V. Y. (Ural State Pedagogical University)

PURSUIT PROBLEM, EUCLIDEAN 3D-SPACE


doi: 10.18698/2309-3684-2024-2-6884


An analytical solution of the pursuit problem in the “predator-prey” system in Euclide-an 3D space for arbitrary initial aiming angles was obtained in the article for the first time. In the process of pursuit, the prey moves uniformly and rectilinearly, the speed vector of the predator is constant in magnitude and is aimed at the prey. The exact solution of the problem is obtained in the form of a parametrically specified spatial pursuit curve. Exact expressions were obtained for other essential characteristics of the pursuit process (pursuit time, coordinates of the prey, length of the pursuit curve, etc.). A realistic computer simulation of the mutual movement of predator and prey in space and time was carried out; the characteristic parameters of the pursuit process are determined. The significant didactic potential of the solved problem of 3D pursuit for the training of future specialists in the field of mechanics and control is noted; the problem for students can serve as a meaningful basis to carry out research projects, courseworks and final qualifying works.


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