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

IF 1.6 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub 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.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

求助全文

约1分钟内获得全文去求助

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

期刊最新文献

Editorial Board Relating Hamiltonian systems with multiple invariants to generalized Hamiltonian mechanics via multisymplectic geometry The three-point Gaudin model and branched coverings of the Riemann sphere A correspondence between the quantum K theory and quantum cohomology of Grassmannians WDVV solutions associated with the genus one holomorphic differential