On the geometry of Lagrangian and Eulerian descriptions in continuum mechanics

Kadianakis, N

dc.contributor.author	Kadianakis, N	en
dc.date.accessioned	2014-03-01T01:14:55Z
dc.date.available	2014-03-01T01:14:55Z
dc.date.issued	1999	en
dc.identifier.issn	0044-2267	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13274
dc.subject	Continuum Mechanics	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mechanics	en
dc.subject.other	NONLINEAR SOLID MECHANICS	en
dc.subject.other	MATHEMATICAL ASPECTS	en
dc.subject.other	DUAL VARIABLES	en
dc.subject.other	PRINCIPLES	en
dc.title	On the geometry of Lagrangian and Eulerian descriptions in continuum mechanics	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/(SICI)1521-4001(199902)79:2<131::AID-ZAMM131>3.0.CO;2-Q	en
heal.identifier.secondary	http://dx.doi.org/10.1002/(SICI)1521-4001(199902)79:2<131::AID-ZAMM131>3.0.CO;2-Q	en
heal.language	English	en
heal.publicationDate	1999	en
heal.abstract	In this work we present a frame-independent and coordinate-free: approach to the Lagrangian and Eulerian descriptions of the motion of a continuum. Working on manifolds gives us the coordinate-free setting, while the use of classical spacte-time as the ambient space where the continuum moves gives the frame-independent description. This space-time has the minim um possible geometric structure, incorporating only the principle of absolute simultaneity. It does not assume any frames of reference given a priori. Any concept defined is therefore frame-independent. It is shown that many of the kinematical concepts can be defined, in this context. We present both Lagrangian and Eulcrian descriptions and show that many of the formulas concerning the classical relations between, the tensor fields in these two descriptions, hold in this more general framework.	en
heal.publisher	WILEY-V C H VERLAG GMBH	en
heal.journalName	ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik	en
dc.identifier.doi	10.1002/(SICI)1521-4001(199902)79:2<131::AID-ZAMM131>3.0.CO;2-Q	en
dc.identifier.isi	ISI:000078798000006	en
dc.identifier.volume	79	en
dc.identifier.issue	2	en
dc.identifier.spage	131	en
dc.identifier.epage	138	en