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