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Continuum mechanics

  1. Aug 29, 2010 #1
    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.
     
  2. jcsd
  3. Aug 29, 2010 #2
    Look up the Curl of a vector in 2 dimensions

    http://en.wikipedia.org/wiki/Curl_(mathematics [Broken])
     
    Last edited by a moderator: May 4, 2017
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