{"title":"Barycentric Coordinates in the Equilibrium Problem of a Heavy Rough Triangle Suspended on a Pin","authors":"E. A. Nikonova","doi":"10.1134/S0025654424607018","DOIUrl":null,"url":null,"abstract":"<p>A planar equilibrium problem of a heavy homogeneous thin wire triangle suspended on a thin horizontal nail is considered. The existence of equilibrium positions and their dependence on the coefficient of friction and the lengths of the sides of the triangle are studied under the assumption of the presence of a dry friction force acting between the triangle and the nail. The problem is solved in barycentric coordinates associated with the vertex system of the triangle in question. The equilibrium condition is written in a form that allows a cyclic shift of the indices of the quantities included in it to obtain an equilibrium condition for any of the sides of the triangle with which it contacts the nail.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"60 3","pages":"1571 - 1577"},"PeriodicalIF":0.9000,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Solids","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0025654424607018","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
A planar equilibrium problem of a heavy homogeneous thin wire triangle suspended on a thin horizontal nail is considered. The existence of equilibrium positions and their dependence on the coefficient of friction and the lengths of the sides of the triangle are studied under the assumption of the presence of a dry friction force acting between the triangle and the nail. The problem is solved in barycentric coordinates associated with the vertex system of the triangle in question. The equilibrium condition is written in a form that allows a cyclic shift of the indices of the quantities included in it to obtain an equilibrium condition for any of the sides of the triangle with which it contacts the nail.
期刊介绍：
Mechanics of Solids publishes articles in the general areas of dynamics of particles and rigid bodies and the mechanics of deformable solids. The journal has a goal of being a comprehensive record of up-to-the-minute research results. The journal coverage is vibration of discrete and continuous systems; stability and optimization of mechanical systems; automatic control theory; dynamics of multiple body systems; elasticity, viscoelasticity and plasticity; mechanics of composite materials; theory of structures and structural stability; wave propagation and impact of solids; fracture mechanics; micromechanics of solids; mechanics of granular and geological materials; structure-fluid interaction; mechanical behavior of materials; gyroscopes and navigation systems; and nanomechanics. Most of the articles in the journal are theoretical and analytical. They present a blend of basic mechanics theory with analysis of contemporary technological problems.
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