3. Divide equation (10.4) by dt to show that the velocity v = ds/dt is a contravariant vector. Note that the contravaria
Posted: Mon May 23, 2022 12:19 pm
3. Divide equation (10.4) by dt to show that the velocity v = ds/dt is a contravariant vector. Note that the contravariant components of the velocity in polar coordinates are r and 8 (not r and rẻ which are physical components). As we did in (10.11), write the velocity v in polar coordinates in terms of the unit e vectors and in terms of the covariant a vectors. Repeat the problem in spherical coordinates.