Accession Number : AD0652678

Title :   THE PHYSICAL TENSOR AND APPLICATION.

Descriptive Note : Final rept., 1 Nov 65-31 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 second-order 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 quasi-singular bilinear forms, to the quasi-singular and collinear 3-form, and to some quasi-singular 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 multi-relative 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