{"title":"具有微观结构的介质动力学的光滑几何方法","authors":"Ernst Binz , Manuel de Leon , Dan Socolescu","doi":"10.1016/S1251-8069(98)80030-4","DOIUrl":null,"url":null,"abstract":"<div><p>In this note we show that the space of configurations of a medium with a microstructure is a principal bundle over the manifold of embeddings of the underlying macromedia. The structure group is just the group of gauge transformations. An appropriate Lagrangian function is chosen defining the dynamics of the system. The Cosserat media are considered as an example.</p></div>","PeriodicalId":100304,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy","volume":"326 4","pages":"Pages 227-232"},"PeriodicalIF":0.0000,"publicationDate":"1998-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1251-8069(98)80030-4","citationCount":"6","resultStr":"{\"title\":\"On a smooth geometric approach to the dynamics of media with microstructures\",\"authors\":\"Ernst Binz , Manuel de Leon , Dan Socolescu\",\"doi\":\"10.1016/S1251-8069(98)80030-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this note we show that the space of configurations of a medium with a microstructure is a principal bundle over the manifold of embeddings of the underlying macromedia. The structure group is just the group of gauge transformations. An appropriate Lagrangian function is chosen defining the dynamics of the system. The Cosserat media are considered as an example.</p></div>\",\"PeriodicalId\":100304,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy\",\"volume\":\"326 4\",\"pages\":\"Pages 227-232\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1251-8069(98)80030-4\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1251806998800304\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1251806998800304","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On a smooth geometric approach to the dynamics of media with microstructures
In this note we show that the space of configurations of a medium with a microstructure is a principal bundle over the manifold of embeddings of the underlying macromedia. The structure group is just the group of gauge transformations. An appropriate Lagrangian function is chosen defining the dynamics of the system. The Cosserat media are considered as an example.
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