{"title":"On Loeb's criterion of orbital stability of self-excited periodic motions","authors":"I. Boiko","doi":"10.1109/VSS.2018.8460414","DOIUrl":null,"url":null,"abstract":"Loeb's criterion of orbital stability of periodic motions [1] is simple and convenient. It is based on the relationships between the Nyquist plot of the linear part of a nonlinear system and the describing function (DF) of the nonlinearity. However, as shown in the present paper, the original proof is not flawless, as it is based on one assumption, which does not hold. A proof based on the dynamic harmonic balance (DHB) principle and further investigations into this criterion are offered in the present paper.","PeriodicalId":127777,"journal":{"name":"2018 15th International Workshop on Variable Structure Systems (VSS)","volume":"105 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2018 15th International Workshop on Variable Structure Systems (VSS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/VSS.2018.8460414","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
Loeb's criterion of orbital stability of periodic motions [1] is simple and convenient. It is based on the relationships between the Nyquist plot of the linear part of a nonlinear system and the describing function (DF) of the nonlinearity. However, as shown in the present paper, the original proof is not flawless, as it is based on one assumption, which does not hold. A proof based on the dynamic harmonic balance (DHB) principle and further investigations into this criterion are offered in the present paper.
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