{"title":"关于Goryachev–Sretensky陀螺稳态解的可积性和稳定性","authors":"A. A. Kosov, E. I. Semenov","doi":"10.1134/S1990478923030092","DOIUrl":null,"url":null,"abstract":"<p> The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationary\nsolutions are found on the invariant set of the zero level of the area integral, and their stability is\nanalyzed. For the case where the suspension point coincides with the center of mass and the\naction of a gyroscopic moment is of a special type, integration by quadratures is performed.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 3","pages":"557 - 570"},"PeriodicalIF":0.5800,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Integrability and Stability of Stationary Solutions of the Goryachev–Sretensky Gyrostat\",\"authors\":\"A. A. Kosov, E. I. Semenov\",\"doi\":\"10.1134/S1990478923030092\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationary\\nsolutions are found on the invariant set of the zero level of the area integral, and their stability is\\nanalyzed. For the case where the suspension point coincides with the center of mass and the\\naction of a gyroscopic moment is of a special type, integration by quadratures is performed.\\n</p>\",\"PeriodicalId\":607,\"journal\":{\"name\":\"Journal of Applied and Industrial Mathematics\",\"volume\":\"17 3\",\"pages\":\"557 - 570\"},\"PeriodicalIF\":0.5800,\"publicationDate\":\"2023-11-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied and Industrial Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1990478923030092\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923030092","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
On the Integrability and Stability of Stationary Solutions of the Goryachev–Sretensky Gyrostat
The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationary
solutions are found on the invariant set of the zero level of the area integral, and their stability is
analyzed. For the case where the suspension point coincides with the center of mass and the
action of a gyroscopic moment is of a special type, integration by quadratures is performed.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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