{"title":"On the Motion of a Bead on a Rough Hoop Freely Rotating Around a Vertical Diameter","authors":"A. A. Burov, V. I. Nikonov, E. A. Nikonova","doi":"10.1134/S0025654424604440","DOIUrl":null,"url":null,"abstract":"<p>We consider the problem of the motion of a heavy bead strung on a rough heavy hoop freely rotating around a vertical diameter. Non-isolated sets of steady motions of the system are identified, and their bifurcation diagrams are constructed. The dependence of these solutions on an essential parameter of the problem—the constant of the cyclic integral—is studied. The results obtained are compared with the results obtained previously for the case when a rough hoop rotates around a vertical diameter with a constant angular velocity. Typical phase portraits are constructed for various combinations of system parameters.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 6","pages":"3347 - 3359"},"PeriodicalIF":0.9000,"publicationDate":"2025-03-09","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/S0025654424604440","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
We consider the problem of the motion of a heavy bead strung on a rough heavy hoop freely rotating around a vertical diameter. Non-isolated sets of steady motions of the system are identified, and their bifurcation diagrams are constructed. The dependence of these solutions on an essential parameter of the problem—the constant of the cyclic integral—is studied. The results obtained are compared with the results obtained previously for the case when a rough hoop rotates around a vertical diameter with a constant angular velocity. Typical phase portraits are constructed for various combinations of system parameters.
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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