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Extremals and Isoperimetric Extremals of the Rotations in the Plane

Jan Krizek, , Patrik Peska, Lenka Ryparova

Abstract: In the paper we study the extremals and isoperimetric extremals of the rotations in the plane. We found that extremals of the rotations in the plane are arbitrary curves. By studying the Euler-Poisson equations for extended variational problems, we found that the isoperimetric extremals of the rotations in the Euclidian plane are straight lines.
Keywords: extremals / isoperimetric / rotations / plane / curves / Poisson / Euler / Euclidian / straight / equations

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