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Angle measures, general rotations, and roulettes in normed planes

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Abstract

In this paper a special group of bijective maps of a normed plane (or, more generally, even of a plane with a suitable Jordan curve as unit circle) is introduced which we call the group of general rotations of that plane. It contains the isometry group as a subgroup. The concept of general rotations leads to the notion of flexible motions of the plane, and to the concept of Minkowskian roulettes. As a nice consequence of this new approach to motions the validity of strong analogues to the Euler-Savary equations for Minkowskian roulettes is proved.

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Notes

  1. As the Riemannian one.

  2. Normality means the so-called Birkhoff orthogonality of the Minkowski plane.

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Author information

Authors and Affiliations

  1. CEFET/RJ Campus Nova Friburgo, Nova Friburgo, Brazil

    Vitor Balestro

  2. Instituto de Matemática e Estatística, UFF, Niterói, Brazil

    Vitor Balestro

  3. Department of Geometry, Budapest University of Technology and Economics, 1521, Budapest, Hungary

    Ákos G. Horváth

  4. Fakultät für Mathematik, Technische Universität Chemnitz, 09107, Chemnitz, Germany

    Horst Martini

  5. Department of Applied Mathematics, Harbin University of Science and Technology, Harbin, 150080, China

    Horst Martini

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  1. Vitor Balestro
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  2. Ákos G. Horváth
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  3. Horst Martini
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Correspondence to Vitor Balestro.

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Balestro, V., Horváth, Á.G. & Martini, H. Angle measures, general rotations, and roulettes in normed planes. Anal.Math.Phys. 7, 549–575 (2017). https://doi.org/10.1007/s13324-016-0155-3

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