线对称刚体运动的几何学

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2025-07-15 DOI:10.1016/j.difgeo.2025.102270

D. Bayril , J.M. Selig

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引用次数: 0

摘要

在这项工作中，重新审视了线对称刚体运动的运动学几何。这些运动是由刚体在直纹曲面的连续产生线中反射而产生的。利用李代数的方法对经典结果进行了重新推导，得到了新的结果。特别地，利用直纹曲面的Sannia框架找到了这些运动的一些加速度特性的结果。所考虑的直纹曲面是由光滑曲线的切线、法线或二法线以及加泰罗尼亚曲面和右圆锥体给出的。

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The geometry of line-symmetric rigid-body motions

In this work the kinematic geometry of line-symmetric rigid-body motions is revisited. These motions are produced by reflecting a rigid body in the successive generator lines of a ruled surface. Classical results are re-derived using methods from Lie algebra and new results are found. In particular, results for some of the acceleration properties of these motions are found using the Sannia frame of the ruled surfaces. The ruled surfaces considered are given by the tangent, normal or binormal lines to smooth curves as well as Catalan surfaces and right conoids.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.