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< A line segment on the plane, equipped with norm $$\|(x_{1}, x_{2})\| = max \{|x_{1}|, |x_{2}|\}$$, is guarded by the defender **D**. The invader **I** wants to reach the line segment but he has to keep the distance from the defender no less than a given constant $$\rho > 0$$. The defender and the invader can move on the whole plane with maximal speed of $$r_{D}$$ and $$r_{I}$$ respectively, where $$r_{I} > r_{D}$$. No further kinematic or dynamic constrains are imposed on the defender and the invader motions. The maximal length of the line segment which can be guarded by the defender is established in this paper.
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> A line segment on the plane, equipped with norm $$\|(x_{1}, x_{2})\| = \max \{|x_{1}|, |x_{2}|\}$$, is guarded by the defender **D**. The invader **I** wants to reach the line segment but he has to keep the distance from the defender no less than a given constant $$\rho > 0$$. The defender and the invader can move on the whole plane with maximal speed of $$r_{D}$$ and $$r_{I}$$ respectively, where $$r_{I} > r_{D}$$. No further kinematic or dynamic constrains are imposed on the defender and the invader motions. The maximal length of the line segment which can be guarded by the defender is established in this paper.
P. Kawęcki, B. Kraska, K. Majcherek, M. Zoła (lecturer: B. Kraska)
(John Paul II Catholic University of Lublin)
Guarding a line segment
A line segment on the plane, equipped with norm 5c7c203d205cmax205c7b7cx_7b17d7c2c207cx_7b27d7c5c7d202424.png)
, is guarded by the defender D. The invader I wants to reach the line segment but he has to keep the distance from the defender no less than a given constant 
. The defender and the invader can move on the whole plane with maximal speed of 
and 
respectively, where 
. No further kinematic or dynamic constrains are imposed on the defender and the invader motions. The maximal length of the line segment which can be guarded by the defender is established in this paper.