- #1

JTC

- 100

- 6

Another fundamentally simple question...

if I go here;

http://www-hep.physics.uiowa.edu/~vincent/courses/29273/metric.pdf

I see how to calculate the metric tensor. The process is totally clear to me.

My question involves LANGUAGE and the ORIGIN

LANGUAGE: Does one say "one calculates the metric tensor that relates the Cartesian coordinate system to the spherical coordinate system?" How should I say that?

ORIGIN: So I can calculate the metric tensor (and, again, please correct my language), that relates the Cartesian and Cylindrical, the Cylindrical and Spherical, etc...

But how does one get the original metric tensor for the Cartesian (the identity matrix)? What doe that relate?

It seems to me I need two coordinate systems to do this process.

As I begin to calculate derivatives (see the fourth equation on that PDF above), what am I taking the derivative of and with respect to what? What gets me the metric tensor for the Cartesian that "starts the ball rolling?" (so to speak)

And while you are at it: Go to Frankel "GEOMETRY OF PHYSICS" and go to the bottom of page xxxiv.

What is he doing? I see x1, u1, x and theta. I see no organization to this. Could someone elaborate what derivatives he is taking?