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