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...

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

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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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...

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

$${\overline{\overline{\sigma}}}=\sigma_{RR}(r)\overline{e_r}\otimes\overline{e_r}+\sigma_{\theta\theta}(\overline{e_\theta}\otimes\overline{e_\theta}+\overline{e_\phi}\otimes\overline{e_\phi}) $$ 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...googlig did not produce satisfactory results...

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

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Caos
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Cauchy stress tensor for a spericallyspherically symmetric problem

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Caos
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