{"title":"Precession Motions of a Gyrostat, Having a Fixed Point, in Three Homogeneous Force Fields","authors":"G. V. Gorr","doi":"10.1134/S002565442470033X","DOIUrl":null,"url":null,"abstract":"<p>The subject of investigation is the problem on precession motions of a gyrostat with a fixed point in three homogeneous force fields. The class of precessions under consideration is characterized by the constancy of the precession angle and by the commensurability of the precession and proper rotation velocities. Equations of motion of a gyrostat are reduced to a system of three second order differential equations with respect to velocities of precession and proper rotation. Integration of these equations is conducted in the case of precessionally isoconic motions (the precession velocity equals to the proper rotation velocity) and in the case of 2 : 1 resonance, when the precession velocity is two times more, than the proper rotation velocity. It is proved that the obtained solutions can be described by elementary functions of time.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 4","pages":"1841 - 1855"},"PeriodicalIF":0.6000,"publicationDate":"2024-12-28","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/S002565442470033X","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
The subject of investigation is the problem on precession motions of a gyrostat with a fixed point in three homogeneous force fields. The class of precessions under consideration is characterized by the constancy of the precession angle and by the commensurability of the precession and proper rotation velocities. Equations of motion of a gyrostat are reduced to a system of three second order differential equations with respect to velocities of precession and proper rotation. Integration of these equations is conducted in the case of precessionally isoconic motions (the precession velocity equals to the proper rotation velocity) and in the case of 2 : 1 resonance, when the precession velocity is two times more, than the proper rotation velocity. It is proved that the obtained solutions can be described by elementary functions of time.
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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