Application of tensor theory in engineering science
From Academic Kids
Tensor theory is extremely useful in advanced engineering theory. It is used to help describe or model many natural phenomena 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:
- 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.
- dynamics of systems of rigid (assumed incompressible) bodies and particles
- stress and strain within elastic bodies
- 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.
