Squared distance function on the configuration space of a planar spider with applications to Hooke energy and Voronoi distance

IF 1.2 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2025-04-01 Epub Date: 2025-01-15 DOI:10.1016/j.geomphys.2025.105424

Maciej Denkowski , Gaiane Panina , Dirk Siersma

引用次数: 0

Abstract

Spider mechanisms are the simplest examples of arachnoid mechanisms, they are one step more complicated than polygonal linkages. Their configuration spaces have been studied intensively, but are yet not completely understood. In the paper we study them using the Morse theory of the squared distance function from the “body” of the spider to some fixed point in the plane. Generically, it is a Morse-Bott function. We list its critical manifolds, describe them as products of polygon spaces, and derive a formula for their Morse-Bott indices. We apply the obtained results to Hooke energy and Voronoi distance.

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平面蜘蛛构形空间上的距离平方函数及其在Hooke能量和Voronoi距离上的应用

蜘蛛机构是最简单的蛛网膜机构，比多边形机构复杂一步。它们的构型空间已被深入研究，但尚未被完全理解。本文利用从蜘蛛“身体”到平面上某个不动点的距离平方函数的莫尔斯理论来研究它们。一般来说，它是一个Morse-Bott函数。我们列出了它的临界流形，将它们描述为多边形空间的乘积，并推导了它们的莫尔斯-博特指数的公式。我们将所得结果应用于胡克能量和沃罗诺伊距离。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity

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