
Accession Number : AD0652678
Title : THE PHYSICAL TENSOR AND APPLICATION.
Descriptive Note : Final rept., 1 Nov 6531 Jan 67,
Corporate Author : TECHNION  ISRAEL INST OF TECH HAIFA DEPT OF MECHANICS
Personal Author(s) : Karni,Zvi
Report Date : 28 FEB 1967
Pagination or Media Count : 57
Abstract : Differential invariants are constructed from the first tensor derivative applied to the position vector, for the undeformed and for the deformed media in space, multiplying an asymmetric secondorder field tensor (stress), and the relations between them established. Techniques permitting the solution of tensor equations as absolute multilinear vector forms are applied to the singular and quasisingular bilinear forms, to the quasisingular and collinear 3form, and to some quasisingular bilinear forms in combination with vectors leading to homogeneous and inhomogeneous differential equations of the first order. The formulation of the electromechanical field equations is preceded by a discussion on the time rate of volume and surface elements in motion, and by the introduction of a spinning material derivative which permits the consideration of a multirelative motion of a continuum element. The general balance in integral form is set up, with the introduction and definition of a flux derivative and a flux potential. The balance of mass, charge, magnetic flux, linear momentum, angular momentum, and energy, are established, leading to the field equations of the electromechanical continuum.
Descriptors : (*FIELD THEORY, DIFFERENTIAL EQUATIONS), (*TENSOR ANALYSIS, INVARIANCE), MOTION, CONTINUUM MECHANICS, MOMENTUM, MATRICES(MATHEMATICS), VECTOR ANALYSIS, THEOREMS, PERMUTATIONS, ELECTRIC FIELDS
Subject Categories : Electricity and Magnetism
Distribution Statement : APPROVED FOR PUBLIC RELEASE