{"title":"Resonance in Multicomponent Linear Systems","authors":"A. A. Lykov, V. A. Malyshev, M. V. Melikian","doi":"10.3103/S0027133021030043","DOIUrl":null,"url":null,"abstract":"<p>We consider a system of many point particles with arbitrary quadratic interaction and a harmonic force acting on a single fixed particle. Necessary and sufficient conditions for resonance and uniform boundedness of trajectories are obtained; and for the case of resonance the late time asymptotics for energy maximum of the system is obtained as well.</p>","PeriodicalId":710,"journal":{"name":"Moscow University Mechanics Bulletin","volume":"76 3","pages":"88 - 93"},"PeriodicalIF":0.3000,"publicationDate":"2021-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow University Mechanics Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.3103/S0027133021030043","RegionNum":0,"RegionCategory":null,"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 a system of many point particles with arbitrary quadratic interaction and a harmonic force acting on a single fixed particle. Necessary and sufficient conditions for resonance and uniform boundedness of trajectories are obtained; and for the case of resonance the late time asymptotics for energy maximum of the system is obtained as well.
期刊介绍：
Moscow University Mechanics Bulletin is the journal of scientific publications, reflecting the most important areas of mechanics at Lomonosov Moscow State University. The journal is dedicated to research in theoretical mechanics, applied mechanics and motion control, hydrodynamics, aeromechanics, gas and wave dynamics, theory of elasticity, theory of elasticity and mechanics of composites.
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