{"title":"修正了顶部运动的数学模型","authors":"R. Usubamatov, S. Kapayeva","doi":"10.15406/iratj.2022.08.00247","DOIUrl":null,"url":null,"abstract":"The mathematical models for the top motions in known publications contain the incorrect expression of the centrifugal torque and do not consider the action of the Coriolis torque generated by the center mass. In reality, the two centrifugal torques, two torques of Coriolis forces, and two changes in the angular momentums formulate the dependency of the angular velocities of the top motions about two axes. The corrected expression of the centrifugal torque and the Coriolis torque generated by the center mass changed the mathematical models for the top motion and its self-stabilization. The new analytical approach for the spinning top motions with the action of all external and inertial torques gives an accurate solution and describes its physics. The derived mathematical models for the spinning top motions and solution represent a good example of the educational process of engineering mechanics.","PeriodicalId":346234,"journal":{"name":"International Robotics & Automation Journal","volume":"258 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The corrected mathematical models for the top motion\",\"authors\":\"R. Usubamatov, S. Kapayeva\",\"doi\":\"10.15406/iratj.2022.08.00247\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The mathematical models for the top motions in known publications contain the incorrect expression of the centrifugal torque and do not consider the action of the Coriolis torque generated by the center mass. In reality, the two centrifugal torques, two torques of Coriolis forces, and two changes in the angular momentums formulate the dependency of the angular velocities of the top motions about two axes. The corrected expression of the centrifugal torque and the Coriolis torque generated by the center mass changed the mathematical models for the top motion and its self-stabilization. The new analytical approach for the spinning top motions with the action of all external and inertial torques gives an accurate solution and describes its physics. The derived mathematical models for the spinning top motions and solution represent a good example of the educational process of engineering mechanics.\",\"PeriodicalId\":346234,\"journal\":{\"name\":\"International Robotics & Automation Journal\",\"volume\":\"258 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-08-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Robotics & Automation Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15406/iratj.2022.08.00247\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Robotics & Automation Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15406/iratj.2022.08.00247","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The corrected mathematical models for the top motion
The mathematical models for the top motions in known publications contain the incorrect expression of the centrifugal torque and do not consider the action of the Coriolis torque generated by the center mass. In reality, the two centrifugal torques, two torques of Coriolis forces, and two changes in the angular momentums formulate the dependency of the angular velocities of the top motions about two axes. The corrected expression of the centrifugal torque and the Coriolis torque generated by the center mass changed the mathematical models for the top motion and its self-stabilization. The new analytical approach for the spinning top motions with the action of all external and inertial torques gives an accurate solution and describes its physics. The derived mathematical models for the spinning top motions and solution represent a good example of the educational process of engineering mechanics.