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The physical components of vectors and tensors
Author(s) -
Truesdell C.
Publication year - 1953
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/zamm.19530331005
Subject(s) - covariant transformation , covariance and contravariance of vectors , scalar (mathematics) , tensor (intrinsic definition) , tensor field , interpretation (philosophy) , mathematics , curvilinear coordinates , pure mathematics , mathematical analysis , geometry , computer science , exact solutions in general relativity , programming language
Physical components of vectors and tensors referred to general curvilinear co‐ordinates are defined and shown to represent quantities possessed of the natural physical dimensions of the field and capable of immediate physical interpretation. It is shown that scalar functions of second order tensors may be expressed directly in terms of the invariants of the physical components. For the case of orthogonal co‐ordinates, a general formula for the physical components of the covariant derivative of a tensor of any order is derived.