Tuesday, March 6, 2018

homework and exercises - Cauchy stress tensor for a spherically symmetric problem



Given a sperically symmetric problem, I am asked to show that its Cauchy stress tensor, in spherical coordinates will assume the form:


$${\overline{\overline{\sigma}}}=\sigma_{RR}(r)\overline{e_r}\otimes\overline{e_r}+\sigma_{\theta\theta}(r)(\overline{e_\theta}\otimes\overline{e_\theta}+\overline{e_\phi}\otimes\overline{e_\phi}) $$ My idea was to say that that tensor must be invariant under all the O(3) transfromation since the physics of this problem must be invariant under rotation. The problem is that I should express the O(3) transformation in spherical coordinates and this is not immediate for me...




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classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...