Recent content by paccali

Yeah, sorry, the problem is in tensor notation, which implies summation symbols, but it's a shorthand.

Here is the other part of the problem, and please help me out with this: \sigma(r)=\sigma_{0}\mathbf{r}\otimes\mathbf{r} where \mathbr{r}=x_{i}i_{i} So, would this be a correct approach?: \bigtriangledown \cdot\sigma_{ij}=\frac{\partial }{\partial x_{k}}\sigma_{0}x_{i}x_{j}i_{i}\otimes...

Homework Statement Calculate the Divergence of a second-order tensor: \sigma _{ij}(x_{i})=\sigma_{0}x_{i}x_{j} Homework Equations \bigtriangledown \cdot \sigma_{ij}=\sigma_{ij'i} The Attempt at a Solution \sigma_{ij'i}=\frac{\partial }{\partial x_{i}}\cdot\sigma_{0}x_{i}x_{j}...

I just found what I did wrong, but thanks for the help nonetheless.

Nevermind, I figured out how to solve the problem using my old differential equations textbook. In case someone is curious, here's what I did: I rearranged the terms so that like terms were on the same side: \frac{dz_{1}}{dt}=-z_{1}^{2} \frac{dz_{1}}{-z_{1}^{2}}=dt I then integrated...

Homework Statement Eulerian velocity: V_{1}=-z_{1}^{2} V_{1}=\frac{dz_{1}}{dt} z_{1}(t=0)=x_{1} This is supposed to become the Lagrangian velocity of: z_{1}=\frac{x_{1}}{1+tx_{1}} I don't understand how to take the Eulerian velocity and transform it to Lagrangian. Homework EquationsThe...