a body has the symmetry that its shape is unchanged by arbitrary rotations around axis, e_3, Show that any second-rank tensor calculated for the body will take the form:

3*3 matrix:

a b 0

-b a 0

0 0 c

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- Apr 18th 2008, 08:27 AMszpengchaosymmetry and tensor
a body has the symmetry that its shape is unchanged by arbitrary rotations around axis, e_3, Show that any second-rank tensor calculated for the body will take the form:

3*3 matrix:

a b 0

-b a 0

0 0 c - Oct 27th 2008, 01:19 PMRebesques
There is Euler's theorem, that says that a rotation around an axis is given by a $\displaystyle 3\times 3$ matrix of the form $\displaystyle \begin{Bmatrix} {\bf A} & 0 \\ 0 & 1 \end{Bmatrix}$, where the matrix $\displaystyle {\bf A}$ is a rotation of the plane.