The inverse problem on Roulettes in normed planes

被引：1

作者：

Balestro, Vitor ^{[1
]}

Horvath, Akos G. ^{[2
]}

Martini, Horst ^{[3
]}

机构：

[1] Univ Fed Fluminense, Inst Matemat & Estat, BR-24210201 Niteroi, RJ, Brazil

[2] Budapest Univ Technol & Econ, Dept Geometry, H-1521 Budapest, Hungary

[3] Tech Univ Chemnitz, Fac Math, D-09107 Chemnitz, Germany

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2019年 / 9卷 / 04期

关键词：

Angle measure; Birkhoff orthogonality; Curvatures; Cycloids; Motion group; Roulettes; 46B20; 51M05; 52A21; 53A04; 53A17; ANGLE MEASURES; MINKOWSKI;

D O I：

10.1007/s13324-019-00343-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：2413 / 2434

页数：22

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