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On the Geometry of Lagrangian and Eulerian Descriptions in Continuum Mechanics
Author(s) -
Kadianakis N.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199902)79:2<131::aid-zamm131>3.0.co;2-q
Subject(s) - eulerian path , frame of reference , mathematics , classical mechanics , reference frame , continuum mechanics , context (archaeology) , lagrangian , motion (physics) , mathematical analysis , frame (networking) , physics , computer science , telecommunications , paleontology , biology
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 minimum 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 Eulerian 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.