Encyclopedia > Application of tensor theory in engineering science

  Article Content

Application of tensor theory in engineering science

Tensor theory is extremely useful in advanced engineering theory. It is used to help describe or model many natural phenomenon such as: physical forces[?], potential fields[?], particle or control element[?] motion, wave propagation, etc.

Constructions notes:

Ai'j'k' = xi'i xj'j ykk' Aijk

Specific examples are:

aeronautical engineering

Navier-Stokes equations Presented in partial differential equation form.

Vorticity is an important quantity in various research, modeling and design calculations regarding lift, drag, and propulsion. It is a tensor quantity defined as: insert gif here when available.

Continuum mechanics

dynamics of systems of rigid (assumed incompressible) bodies and particles

stress and strain within elastic bodies

electromagnetism Maxwell's Equations


Tensor equations to model fluid flow can be derived as follows:
Assume the fluid consists of particles which can be individually tracked as they move in relation to Euclidean 3-space. Thus an individual particle can be tracked as it moves.
We shall use rectangular cartesian coordinates to describe our Euclidean 3 space .... zr

In the Lagrangian method[?], all particles are then described by:

Equation (1) zr=zr(a,t) where a stands for the set of 3 labels representing the 3 dimensions or axis of Euclidean space ... xi,xj,xk.

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
Wheatley Heights, New York

... other races, and 3.73% from two or more races. 11.67% of the population are Hispanic or Latino of any race. There are 1,455 households out of which 43.6% have childr ...

This page was created in 42.6 ms