I'm self-studying Schutz Geometric methods of mathematical physics, having problems with ex. 2.1. page 44.(adsbygoogle = window.adsbygoogle || []).push({});

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

V1=cos(theta), V2=sin(theta)

W1=-sin(theta), W2=cos(theta)

x(r)=r cos(theta)

y(r)=r sin(theta)

x(theta)=cos(theta)

y(theta)=sin(theta)

These parametrics I got from integrating back from the components ofrandtheta

I believe the component ofxshould be (sin(theta))/r, however I get (sin(theta) - r sin(theta))/r.

would appreciate any help

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# Noncoordinate basis vector fields

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