# Trying to derive equation for acceleration in spherical coordinate system

1. Sep 20, 2011

### vweltin

1. The problem statement, all variables and given/known data
I was trying to figure out how to derive acceleration in spherical coordinates, and I realized that I need to find the projection of each spherical unit vector [ e(r), e(θ), and e(φ)] onto each Cartesian unit vector [î, j, and k], but I'm not quite sure as to how to do that. It's pretty intuitive for me to calculate the projections of e(r), but the other components confuse me a bit.

2. Relevant equations
see attached image

3. The attempt at a solution
I've attached the work I've done so far as an image (I didn't mean for that ' near the î on the bottom to be there..)

2. Sep 23, 2011

### omoplata

http://en.wikipedia.org/wiki/Unit_vectors#Spherical_coordinates" are the unit vectors in the spherical coordinate system from wikipedia. Your $\hat{e_r}$ is given as $\hat{r}$, $\hat{e_\theta}$ is given as $\hat{\theta}$ and $\hat{e_\phi}$ is given as $\hat{\psi}$.

It looks to me that your $\hat{e_\theta}$ is drawn incorrectly in the diagram. Is it drawn to go straight in to the page?

Last edited by a moderator: Apr 26, 2017