How was the matrix in the attachment found

[LSMOG]

Main Question or Discussion Point

I understand the dot product of e_i.e_j, but I can't find the matrix components.

 

[martinbn]

I understand the dot product of e_i.e_j, but I can't find the matrix components.

The matrix components are these dot products.

 

[LSMOG]

Thanks. I've managed to find the matrix above by finding the dot products. Now how was ds² = dr²+r²dθ²+r² sin²θ dΦ² found?

 

[robphy]

http://hyperphysics.phy-astr.gsu.edu/hbase/sphc.html

http://mathworld.wolfram.com/SphericalCoordinates.html

 

[sweet springs]

You can get it by inserting
$$x=r\ sin\theta\ cos\phi$$
$$y=r\ sin\theta\ sin\phi$$
$$z=r\ cos\ \theta$$
into
$$dx^2+dy^2+dz^2$$

 

[LSMOG]

You can get it by inserting
$$x=r\ sin\theta\ cos\phi$$
$$y=r\ sin\theta\ sin\phi$$
$$z=r\ cos\ \theta$$
into
$$dx^2+dy^2+dz^2$$

Thank you. But you you gave x, y and z in spherical coordinates, according to your last expression, I need dx, dy and dx in spherical coordinates.

 

[Dr Transport]

Thank you. But you you gave x, y and z in spherical coordinates, according to your last expression, I need dx, dy and dx in spherical coordinates.

do the derivatives