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The inverse problem on Roulettes in normed planes

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Abstract

We investigate an inverse problem referring to roulettes in normed planes, thus generalizing analogous results of Bloom and Whitt on the Euclidean subcase. More precisely, we prove that a given curve can be traced by rolling another curve along a line if two natural conditions are satisfied. Our access involves details from a metric theory of trigonometric functions, which was recently developed for normed planes. Based on this, our approach differs from other ones in the literature.

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Notes

  1. In contrast to the notation of the paper [5], \([\cdot ,\cdot ]\) is not a non-degenerate symplectic bilinear form!

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, 24210201, Brazil

    Vitor Balestro

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

    Ákos G. Horváth

  3. Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    Horst Martini

Authors
  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. The inverse problem on Roulettes in normed planes. Anal.Math.Phys. 9, 2413–2434 (2019). https://doi.org/10.1007/s13324-019-00343-5

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  • DOI: https://doi.org/10.1007/s13324-019-00343-5

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