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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2020, Volume 26, Number 4, Pages 76–82
DOI: https://doi.org/10.21538/0134-4889-2020-26-4-76-82
(Mi timm1767)
 

An object moving in $\mathbb R^2$ with a high-speed destructive miniobject and an unfriendly solid observer

V. I. Berdyshev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
References:
Abstract: We propose a model for the motion in a given corridor $Y\subset \mathbb{R}^2$ of an object $t$ equipped with a high-speed destructive miniobject in the presence of a solid unfriendly observer $f$. In $\mathbb{R}^2\backslash Y$ there is a subset $G$ that obstructs visibility and motion. For safety reasons, the observer sticks to neighborhoods of the angles and convex fragments of the boundary of $G$. The trajectory of $t$ is a curve $\mathcal{T}\subset Y$ with a given speed regime $v_t$ of the motion along it. The possibilities for the observer to track the object in a safe mode and for the object to avoid the observation depend on the positions of the observer and the object. We characterize the positions in which, for any $\mathcal{T}$, the object can choose a regime $v_t$ enabling the avoidance of observation and the positions guaranteeing that the observer can see a part of the trajectory.
Keywords: navigation, trajectory, observer, moving object.
Funding agency Grant number
Ural Mathematical Center
This study is a part of the research carried out at the Ural Mathematical Center.
Received: 25.08.2020
Revised: 23.10.2020
Accepted: 26.10.2020
Bibliographic databases:
Document Type: Article
UDC: 519.62
MSC: 00A05
Language: Russian
Citation: V. I. Berdyshev, “An object moving in $\mathbb R^2$ with a high-speed destructive miniobject and an unfriendly solid observer”, Trudy Inst. Mat. i Mekh. UrO RAN, 26, no. 4, 2020, 76–82
Citation in format AMSBIB
\Bibitem{Ber20}
\by V.~I.~Berdyshev
\paper An object moving in $\mathbb R^2$ with a high-speed destructive miniobject and an unfriendly solid observer
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2020
\vol 26
\issue 4
\pages 76--82
\mathnet{http://mi.mathnet.ru/timm1767}
\crossref{https://doi.org/10.21538/0134-4889-2020-26-4-76-82}
\elib{https://elibrary.ru/item.asp?id=44314660}
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  • https://www.mathnet.ru/eng/timm/v26/i4/p76
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    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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