{"title":"Stability of Floating of Vessels with Cross Sections in the Form of Elliptical and Hyperbolic Segments","authors":"A. S. Smirnov, I. A. Kravchinsky","doi":"10.1134/s1063454124010126","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Two problems on the stability of the trivial equilibrium position of floating vessels with cross sections in the form of elliptic and hyperbolic segments are considered. Examples on the stability of floating bodies are reviewed, and the key principles of its investigation by analytical statics methods are outlined. For each of the presented problems, by means of quite serious mathematical constructions, an exact expression for the potential energy is obtained within the accepted configuration, and its quadratic approximation near the equilibrium state under study is calculated. On its basis, the stability conditions of the equilibrium state in terms of three dimensionless parameters are determined and the limiting cases are also analyzed. The intermediate expressions and final results obtained as a result of discussion of each of the problems are compared, and their common and distinctive features are identified. The found solutions are illustrated as families of boundaries of stability regions on the plane of two dimensionless parameters at different values of the third parameter. These results are of fundamental theoretical importance and can prove useful for practical applications.</p>","PeriodicalId":43418,"journal":{"name":"Vestnik St Petersburg University-Mathematics","volume":"101 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik St Petersburg University-Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1063454124010126","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Two problems on the stability of the trivial equilibrium position of floating vessels with cross sections in the form of elliptic and hyperbolic segments are considered. Examples on the stability of floating bodies are reviewed, and the key principles of its investigation by analytical statics methods are outlined. For each of the presented problems, by means of quite serious mathematical constructions, an exact expression for the potential energy is obtained within the accepted configuration, and its quadratic approximation near the equilibrium state under study is calculated. On its basis, the stability conditions of the equilibrium state in terms of three dimensionless parameters are determined and the limiting cases are also analyzed. The intermediate expressions and final results obtained as a result of discussion of each of the problems are compared, and their common and distinctive features are identified. The found solutions are illustrated as families of boundaries of stability regions on the plane of two dimensionless parameters at different values of the third parameter. These results are of fundamental theoretical importance and can prove useful for practical applications.
期刊介绍：
Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.
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