Example 1 edit


Euler's second law for the conservation of angular momentum


The divergence theorem


The equilibrium equation (Cauchy's first law)




Solution edit

Let us first look at the first term of equation~(1) and apply the divergence theorem (2). Thus,


Plugging this back into equation~(1) gives


Therefore, bringing all terms to the left hand side,


Using the equilibrium equations~(3), equation~(5) reduces to


Since this holds for any  , we have


If you work this expression out, you will see that  . Hence, the stress tensor is symmetric.