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)

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

would appreciate any help

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Noncoordinate basis vector fields

**Physics Forums | Science Articles, Homework Help, Discussion**