{"title":"The principles of Lagrange–d’Alembert and Hamilton applied to a rigid bar subject to nonholonomic constraints","authors":"Alessandro Tiero","doi":"10.1007/s00707-024-04081-z","DOIUrl":null,"url":null,"abstract":"<div><p>It is well known that the Lagrange–d’Alembert and Hamilton principles, which are widely used to derive the laws of motion for nonholonomic systems, are not equivalent and that, in some cases, the equations of motion derived from them differ. The aim of this paper is to illustrate these differences by comparing the solutions of the dynamic equations derived from these principles in a simple nonholonomic system.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 1","pages":"91 - 103"},"PeriodicalIF":2.3000,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00707-024-04081-z","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
It is well known that the Lagrange–d’Alembert and Hamilton principles, which are widely used to derive the laws of motion for nonholonomic systems, are not equivalent and that, in some cases, the equations of motion derived from them differ. The aim of this paper is to illustrate these differences by comparing the solutions of the dynamic equations derived from these principles in a simple nonholonomic system.
期刊介绍：
Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.
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