{"title":"Canonical equations for generalized Chaplygin systems and Herglotz-type Noether theorems","authors":"Yi Zhang","doi":"10.1007/s00707-024-04204-6","DOIUrl":null,"url":null,"abstract":"<div><p>Herglotz’s principle is suitable for dealing with nonconservative phenomena. It is an extension of Hamilton’s principle. The generalized Chaplygin canonical equations are derived from Herglotz principle for nonconservative systems with nonholonomic constraints. The variational equation of Hamilton–Herglotz action for generalized Chaplygin systems is derived by using the Chetaev condition of constraints on virtual displacements. From this, two formulas of non-isochronous variation of the action are deduced. The definitions of Herglotz-type Noether symmetric transformation and quasi-symmetric transformation in phase space are given, and the criterion (i.e., generalized Noether identity) is derived by using total variational formula, and the Herglotz-type Noether-conserved quantities are given. Finally, a nonconservative nonholonomic system is investigated, the Herglotz-type generalized Chaplygin equation and generalized Noether identity are set up, and conservation laws are found by using the theorems we obtained, and the validity of the results is verified.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1061 - 1070"},"PeriodicalIF":2.3000,"publicationDate":"2025-01-08","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/s00707-024-04204-6","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
Herglotz’s principle is suitable for dealing with nonconservative phenomena. It is an extension of Hamilton’s principle. The generalized Chaplygin canonical equations are derived from Herglotz principle for nonconservative systems with nonholonomic constraints. The variational equation of Hamilton–Herglotz action for generalized Chaplygin systems is derived by using the Chetaev condition of constraints on virtual displacements. From this, two formulas of non-isochronous variation of the action are deduced. The definitions of Herglotz-type Noether symmetric transformation and quasi-symmetric transformation in phase space are given, and the criterion (i.e., generalized Noether identity) is derived by using total variational formula, and the Herglotz-type Noether-conserved quantities are given. Finally, a nonconservative nonholonomic system is investigated, the Herglotz-type generalized Chaplygin equation and generalized Noether identity are set up, and conservation laws are found by using the theorems we obtained, and the validity of the results is verified.
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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