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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2021 Volume 27, Number 2, Pages 49–58 (Mi timm1813)

An Object with a Striking Device and a Hostile Observer in Three-Dimensional Space

V. I. Berdyshev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: An autonomous object with a high-speed striking device is moving under observation, and a bodily observer has to hide from the device behind convex fragments of the surrounding area. The observer tracks the motion of the object in a safe mode. The task of the object is to evade observation by choosing its speed of motion. The observer's trajectory allowing to follow the object on the largest possible part of the object's trajectory is constructed.

Keywords: navigation, optimal trajectory, moving object, bodily observer.

UDC: 519.62

MSC: 00A05

Received: 05.03.2021
Revised: 02.04.2021
Accepted: 12.04.2021

DOI: 10.21538/0134-4889-2021-27-2-49-58


 English version:
Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2022, 317, suppl. 1, S27–S36

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© Steklov Math. Inst. of RAS, 2025