Angle measures, general rotations, and roulettes in normed planes

被引：4
作者：
Balestro, Vitor [1 ,2 ]
Horvath, Akos G. [3 ]
Martini, Horst [4 ,5 ]
机构：
[1] CEFET RJ, Campus Nova Friburgo, Nova Friburgo, Brazil
[2] Univ Fed Fluminense, Inst Matemat & Estat, Niteroi, RJ, Brazil
[3] Budapest Univ Technol & Econ, Dept Geometry, H-1521 Budapest, Hungary
[4] Tech Univ Chemnitz, Fak Math, D-09107 Chemnitz, Germany
[5] Harbin Univ Sci & Technol, Dept Appl Math, Harbin 150080, Heilongjiang, Peoples R China
来源：
ANALYSIS AND MATHEMATICAL PHYSICS | 2017年 / 7卷 / 04期
关键词：
Angle measure; Busemann curvature; Euler-Savary equations; Finsler space; Normed plane; Roulettes; CONVEX MINKOWSKI PLANES; EULER-SAVARY FORMULA; INFINITESIMAL RIGIDITY; SPACES; MOTION; POINT;
D O I：
10.1007/s13324-016-0155-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：549 / 575
页数：27
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