{"title":"在摩擦力可忽略的情况下,倾斜大角度摆可使小车产生无休止的直线运动","authors":"Dennis P. Allen, C. Provatidis","doi":"10.37394/232011.2022.17.23","DOIUrl":null,"url":null,"abstract":"We present the mechanics for the oscillation of an inclined large-angle pendulum-drive attached to a cart which is allowed to perform translation in one direction only. Neglecting the overall friction, the application of Newton’s second law shows that the oscillation of the pendulum is continuously converted into oscillating linear motion thus achieving a travel of infinite length. It is also shown that the frequency depends on the usual data of any pendulum plus the mass of the cart on which it is attached. After the determination of a novel effective pendulum length, a closed-form accurate analytical expression is presented for the amplitude of the pendulum, whereas semi-analytical formulas are provided for the period as well as the time-variation of the large azimuthal-like angle. Moreover, a simple expression was found for the position of the cart in terms of the azimuthal angle of the pendulum and the elapsed time. The extraction of the analytical formulas was facilitated by a computer model programmed in MATLAB®.","PeriodicalId":53603,"journal":{"name":"WSEAS Transactions on Applied and Theoretical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Inclined Large-angle Pendulum May Produce Endless Linear Motion of a Cart When Friction is Negligible\",\"authors\":\"Dennis P. Allen, C. Provatidis\",\"doi\":\"10.37394/232011.2022.17.23\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present the mechanics for the oscillation of an inclined large-angle pendulum-drive attached to a cart which is allowed to perform translation in one direction only. Neglecting the overall friction, the application of Newton’s second law shows that the oscillation of the pendulum is continuously converted into oscillating linear motion thus achieving a travel of infinite length. It is also shown that the frequency depends on the usual data of any pendulum plus the mass of the cart on which it is attached. After the determination of a novel effective pendulum length, a closed-form accurate analytical expression is presented for the amplitude of the pendulum, whereas semi-analytical formulas are provided for the period as well as the time-variation of the large azimuthal-like angle. Moreover, a simple expression was found for the position of the cart in terms of the azimuthal angle of the pendulum and the elapsed time. The extraction of the analytical formulas was facilitated by a computer model programmed in MATLAB®.\",\"PeriodicalId\":53603,\"journal\":{\"name\":\"WSEAS Transactions on Applied and Theoretical Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"WSEAS Transactions on Applied and Theoretical Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37394/232011.2022.17.23\",\"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":"WSEAS Transactions on Applied and Theoretical Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/232011.2022.17.23","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
Inclined Large-angle Pendulum May Produce Endless Linear Motion of a Cart When Friction is Negligible
We present the mechanics for the oscillation of an inclined large-angle pendulum-drive attached to a cart which is allowed to perform translation in one direction only. Neglecting the overall friction, the application of Newton’s second law shows that the oscillation of the pendulum is continuously converted into oscillating linear motion thus achieving a travel of infinite length. It is also shown that the frequency depends on the usual data of any pendulum plus the mass of the cart on which it is attached. After the determination of a novel effective pendulum length, a closed-form accurate analytical expression is presented for the amplitude of the pendulum, whereas semi-analytical formulas are provided for the period as well as the time-variation of the large azimuthal-like angle. Moreover, a simple expression was found for the position of the cart in terms of the azimuthal angle of the pendulum and the elapsed time. The extraction of the analytical formulas was facilitated by a computer model programmed in MATLAB®.
期刊介绍:
WSEAS Transactions on Applied and Theoretical Mechanics publishes original research papers relating to computational and experimental mechanics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with fluid-structure interaction, impact and multibody dynamics, nonlinear dynamics, structural dynamics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.