Coordinate Curvilinear Systems

Question 1

What is the format for the position vector of the Cartesian system?

Answer 1

r⃗ = xî + yĵ + zk̂

Question 2

What is the formula for any unit tangent vectors e^→_u, e^→_v, and e^→_w?

Answer 2

Here

Question 3

What is the curl in a curvilinear system?

Answer 3

Here

Question 4

What are the scale factors for a cylindrical coordinate system?

Answer 4

Recall, h_u = |e^→|,
But importantly:
h_p = 1, h_θ = p, h_z = 1

Question 5

What is the scale factor (h_blah) for a spherical curvilinear system?

Answer 5

h_p = 1, h_θ = p, h_z = psinθ