{"title":"Approximate Noether’s symmetry and conservation laws for approximate Lagrangian systems on time scales","authors":"S. X. Jin, X. W. Chen, Y. M. Li","doi":"10.1007/s00707-025-04263-3","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, the approximate Noether symmetries and conservation laws for approximate Lagrangian systems on time scales are discussed and presented. The Hamilton principle of approximate Lagrangian systems on time scales is given, and the approximate Lagrange equations for approximate Lagrangian systems on time scales are established. The Noether identities on time scales are given, the relationship between the approximate Noether symmetries and approximate conservation laws on time scales are established, the approximate inverse Noether theorems on time scales are obtained. Special cases such as the classical approximate Lagrangian systems and the discrete approximate Lagrangian systems are discussed. Finally, one example is given to illustrate the application of the results.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 3","pages":"2065 - 2076"},"PeriodicalIF":2.3000,"publicationDate":"2025-02-24","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/s00707-025-04263-3","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
In this paper, the approximate Noether symmetries and conservation laws for approximate Lagrangian systems on time scales are discussed and presented. The Hamilton principle of approximate Lagrangian systems on time scales is given, and the approximate Lagrange equations for approximate Lagrangian systems on time scales are established. The Noether identities on time scales are given, the relationship between the approximate Noether symmetries and approximate conservation laws on time scales are established, the approximate inverse Noether theorems on time scales are obtained. Special cases such as the classical approximate Lagrangian systems and the discrete approximate Lagrangian systems are discussed. Finally, one example is given to illustrate the application of the results.
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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