edited it kind of
user99917

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 invarianinvariant 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...googling did not produce satisfactory results...

Post Closed as "Not suitable for this site" by Kyle Kanos, HDE 226868, DilithiumMatrix, ACuriousMind, Gert
Caos
• 785
• 6
• 26

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

$${\overline{\overline{\sigma}}}=\sigma_{RR}(r)\overline{e_r}\otimes\overline{e_r}+\sigma_{\theta\theta}(\overline{e_\theta}\otimes\overline{e_\theta}+\overline{e_\phi}\otimes\overline{e_\phi})$$$${\overline{\overline{\sigma}}}=\sigma_{RR}(r)\overline{e_r}\otimes\overline{e_r}+\sigma_{\theta\theta}(r)(\overline{e_\theta}\otimes\overline{e_\theta}+\overline{e_\phi}\otimes\overline{e_\phi})$$ My idea was to say that that tensor must be invarian 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...googliggoogling did not produce satisfactory results...

edited title
Caos
• 785
• 6
• 26

Caos
• 785
• 6
• 26