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Aerospace Instrument-Making

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SOLUTION OF THE PURSUIT-EVASION PROBLEM FOR TWO STRATEGIES OF MOVEMENT USING GEOMETRIC INVARIANTS
V.M. Khachumov, M.V. Khachumov

The paper proposes new statements of pursuit-evasion problems on the plane for two strategies of player movement and considers schemes for their solution based on the construction of Apollonius circles, which are geometric invariants. Variants are considered when the pursuer moves along a straight line, and the evader along a circle or both players move along circular arcs, which leads to equations with inverse trigonometric functions when solving the problem. A theorem is proved on the geometric location of the meeting points of the pursuer and the evader when moving along arcs of circles. An approximate solution of the pursuit-evasion problem is given using the Huygens formula. The proposed formulations can be considered as an addition to the set of possible strategies for the movement of the sides in differential games.
Keywords: differential games, pursuit and evasion, Apollonius circle, invariant, motion strategy, Huygens’ formula.


DOI: 10.25791/aviakosmos.9.2021.1241

Pp. 46-54.

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