Why is it that in general geodesics are paths of stationary character

[Thrice]

Well since the denizens of the relativity forum don't like me, I thought I might ask here see if I get better replies.1) Why is it that in general geodesics are paths of "stationary character" rather than minimum?

2) http://img366.imageshack.us/img366/3280/math30016nx.jpg

I can't quite follow equation 11.16. Specifically how they differentiate dxm/ds in the denominator.
Shouldn't be necessary, but for reference, the following page is http://img353.imageshack.us/img353/6488/math30024mk.jpg" .

 

[nrqed]

Well since the denizens of the relativity forum don't like me, I though I might ask here see if I get better replies.

They have been mean?

1) Why is it that in general geodesics are paths of "stationary character" rather than minimum?

They impose that it's an extremum (functional derivative is zero) so it could be either a min or a max.

2) http://img366.imageshack.us/img366/3280/math30016nx.jpg

I can't quite follow equation 11.16. Specifically how they differentiate dxm/ds in the denominator.
Shouldn't be necessary, but for reference, the following page is http://img353.imageshack.us/img353/6488/math30024mk.jpg" .

They do not differentiate dxm/ds..they differentiate with respect to dxm/ds. You must treat the *entire* combination dxm/ds as your variable and differentiate with respect to it (So, calling the variable x, L is essentially ${\sqrt{ g_{kn} x^k x^n}}$).

Pat

 

[Thrice]

No they weren't mean. They just gave me the silent treatment.

Thanks. It's a lot clearer now.