Main Page | See live article | Alphabetical index 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 Hydrodynamics 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. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.