Question

I'm trying to determine the following vector math..

Answer 1

The original problem pertains to Lagrangian and Hamiltonian comparisons. The end result for this part is that I want to see if the equation obtained: \[m\ddot{\vec{r}} = m\dot{\vec{r}}\times(\nabla \times (\vec{\Omega}\times\vec{r}) + \nabla (m/2)(\vec{\Omega}\times\vec{r})^2\]can be turned into \[m\ddot{\vec{r}} = 2m \dot{\vec{r}}\times\vec{\Omega}+m(\vec{\Omega}\times\vec{r})\times\vec{\Omega}\]

Answer 2

Using either vector identities, or breaking it down piece by piece. I've solved that the first term of the former equation should be equal to the first term in the latter. Now I'm just to convert the remaining term

Answer 3

I was trying to discern particular points to see if any made sense and I could map it out from one to the other, but I've failed to see the connections

Answer 4

@Kainui this is what I was leading up to before, if you have any insight, it would be much appreciated