THE PHYSICAL TENSOR AND APPLICATION.

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.

Document Details

Document Type
Technical Report
Publication Date
Feb 28, 1967
Accession Number
AD0652678

Entities

People

  • Zvi Karni

Organizations

  • Technion – Israel Institute of Technology

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Angular Momentum
  • Differential Equations
  • Equations
  • Integrals
  • Linear Momentum
  • Magnetic Flux
  • Materials
  • Mathematics
  • Momentum
  • Partial Differential Equations
  • Relative Motion

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.
  • Linear Algebra

Technology Areas

  • Microelectronics
  • Space