- #1

MrBillyShears

Gold Member

- 14

- 0

## Main Question or Discussion Point

Alright, so I was reading up on tensors and such with non-Cartesian coordinate systems all day but now I'm a bit tired an confused so you'll have to forgive me if it's a stupid question. So to express the dot product in some coordinate system, it's:

[itex]g(\vec{A}\,,\vec{B})=A^aB^bg_{ab}[/itex]

And, if we're dealing with polar coordinates, then the metric is:

[itex]g_{ab}=\begin{pmatrix}1&0\\0&r^2\end{pmatrix}[/itex]

Alright, so the dot product is:

[itex]A^1B^1+(r)^2A^2B^2[/itex]

But which r? I know I'm probably only confused because I'm so tired right now, but both A and B have r's, do't they? Which r is used to compute this?

Remember, I'm just a student at this, so don't get too technical in the response, and sorry for any typos.

Thanks!

[itex]g(\vec{A}\,,\vec{B})=A^aB^bg_{ab}[/itex]

And, if we're dealing with polar coordinates, then the metric is:

[itex]g_{ab}=\begin{pmatrix}1&0\\0&r^2\end{pmatrix}[/itex]

Alright, so the dot product is:

[itex]A^1B^1+(r)^2A^2B^2[/itex]

But which r? I know I'm probably only confused because I'm so tired right now, but both A and B have r's, do't they? Which r is used to compute this?

Remember, I'm just a student at this, so don't get too technical in the response, and sorry for any typos.

Thanks!