Methods for observing an object moving in under conditions of its opposition

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Abstract

We propose ways of action of the observer f when tracking an object t moving in 3 along the shortest trajectory T enveloping the set Gi of convex sets. The object has velocity mini-objects that pose a hazard to the observer. The means of observation depend on the geometric properties of the sets Gi and the trajectory T. The observer's task – to track the motion of the object over as much of the trajectory T as possible.

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About the authors

V. I. Berdyshev

Krasovskii Institute of Mathematics and Mechanics Ural Branch of the Russian Academy of Sciences

Author for correspondence.
Email: bvi@imm.uran.ru

Academicain of the RAS

Russian Federation, Yekaterinburg

References

  1. Милка А.Д. Кратчайшие линии на выпуклых поверхностях // Мат. заметки. 1984. Т. 35. Вып. 4. С. 617–635.
  2. Люстерник Л.A. Геодезические линии. М.–Л.: Гос. изд-во технико-теорет. литературы, 1940. 50 с.
  3. Clarcson J.A. Uniformly convex spaces // Trans. Amer. Math. Soc. 1936. V. 40. P. 396–414.

Supplementary files

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2. Fig. 1. The bold line shows the trajectory.

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3. Fig. 2. The bold line shows the trajectory, the thin line shows the circles of radius and the boundary.

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4. Fig. 3. The trajectory is shown by the bold line, the circumference of the torus by the thin line.

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