Continuum mechanics

stanley.st

Hello!

I read somewhere about intro to continuum mechanics. There was a vector [tex]\vec{\mu}[/tex] and displacement vector [tex]\delta\vec{\mu}[/tex]. As vector [tex]\vec{\mu}[/tex] move, it will get new position

[tex]\vec{\mu}'=\vec{\mu}+\delta\vec{\mu}[/tex]

[tex]\vec{\mu}'=\vec{\mu}+\frac{\partial\vec{\mu}}{\partial x_i}\delta x_i=\vec{\mu}+\left(\frac{\partial\vec{\mu}}{\partial x_i}+\frac{1}{2}\frac{\partial\vec{\mu}}{\partial x_j}-\frac{1}{2}\frac{\partial\vec{\mu}}{\partial x_j}\right)\delta x_i=\vec{\mu}+\left[\frac{1}{2}\left(\frac{\partial\vec{\mu}}{\partial x_i}+\frac{\partial\vec{\mu}}{\partial x_j}\right)+\frac{1}{2}\left(\frac{\partial\vec{\mu}}{\partial x_i}-\frac{\partial\vec{\mu}}{\partial x_j}\right)\right]\delta x_i[/tex]

Last component

[tex]\frac{1}{2}\left(\frac{\partial\vec{\mu}}{\partial x_i}-\frac{\partial\vec{\mu}}{\partial x_j}\right)[/tex]

represent rotation. Can you explain me that? I don't understand this rotation.

Studiot

Look up the Curl of a vector in 2 dimensions

http://en.wikipedia.org/wiki/Curl_(mathematics)