{"title":"滚轴自行车的非线性动力学","authors":"Ivan A. Bizyaev, Ivan S. Mamaev","doi":"10.1134/S1560354724530017","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we consider the dynamics of a roller\nbicycle on a horizontal plane. For this bicycle we derive a\nnonlinear system of equations of motion in a form that allows\nus to take into account the symmetry of the system in a\nnatural form. We analyze in detail the stability of straight-line\nmotion depending on the parameters of the bicycle.\nWe find numerical evidence that, in addition to stable straight-line motion,\nthe roller bicycle can exhibit other, more complex,\ntrajectories for which the bicycle does not fall.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"29 5","pages":"728 - 750"},"PeriodicalIF":0.8000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonlinear Dynamics of a Roller Bicycle\",\"authors\":\"Ivan A. Bizyaev, Ivan S. Mamaev\",\"doi\":\"10.1134/S1560354724530017\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we consider the dynamics of a roller\\nbicycle on a horizontal plane. For this bicycle we derive a\\nnonlinear system of equations of motion in a form that allows\\nus to take into account the symmetry of the system in a\\nnatural form. We analyze in detail the stability of straight-line\\nmotion depending on the parameters of the bicycle.\\nWe find numerical evidence that, in addition to stable straight-line motion,\\nthe roller bicycle can exhibit other, more complex,\\ntrajectories for which the bicycle does not fall.</p></div>\",\"PeriodicalId\":752,\"journal\":{\"name\":\"Regular and Chaotic Dynamics\",\"volume\":\"29 5\",\"pages\":\"728 - 750\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Regular and Chaotic Dynamics\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1560354724530017\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S1560354724530017","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
In this paper we consider the dynamics of a roller
bicycle on a horizontal plane. For this bicycle we derive a
nonlinear system of equations of motion in a form that allows
us to take into account the symmetry of the system in a
natural form. We analyze in detail the stability of straight-line
motion depending on the parameters of the bicycle.
We find numerical evidence that, in addition to stable straight-line motion,
the roller bicycle can exhibit other, more complex,
trajectories for which the bicycle does not fall.
期刊介绍：
Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.
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