2nd last para of my previous note should read (that's what happens when you type too fast):
Geometrically, if you travel from P along V curve (delta l = e) to point R, then along W curve (delta m = e) to point A, and travel from P along W curve (delta m = e) to Q, then along V curve (delta l...
Well according to Schutz, "any linearly indepedent set of vector fields can serve as a basis, and one can easily show that not all of them are derivable from coordinate systems". The basic test is whether the fields commute. So if:
l and m are independent parameters that generate integral...
I'm self-studying Schutz Geometric methods of mathematical physics, having problems with ex. 2.1. page 44.
r=cos(theta)x+sin(theta)y
theta=-sin(theta)x+cos(theta)y
show this is non-coordinate basis, i.e. show commutator non-zero.
I try to apply his formula 2.7, assuming...
I'm self-studying Schutz Geometric methods of mathematical physics, having problems with ex. 2.1. page 44.
r=cos(theta)x+sin(theta)y
theta=-sin(theta)x+cos(theta)y
show this is non-coordinate basis, i.e. show commutator non-zero.
I try to apply his formula 2.7, assuming...