Verify the following relations for cylindrical coordinates u = r, v = 0, w = z: a) the surfaces r= const, 0 = const, z = const form a triply orthogonal family, and a(x, y, z) a(r, 0, z) b) the element of are length is given by ds² = dr² + r?d0² + dz?; c) the components of a vector p are given by Pr = Px cos0 + py sin 0, po =-Px sin 0 + Py cos 0, P: = Pzi
Verify the following relations for cylindrical coordinates u = r, v = 0, w = z: a) the surfaces r= const, 0 = const, z = const form a triply orthogonal family, and a(x, y, z) a(r, 0, z) b) the element of are length is given by ds² = dr² + r?d0² + dz?; c) the components of a vector p are given by Pr = Px cos0 + py sin 0, po =-Px sin 0 + Py cos 0, P: = Pzi
Related questions
Question
Please provide typed answer.
I NEED TYPED ANSWERS.
Thank you.
Transcribed Image Text:Verify the following relations for cylindrical coordinates u = r, v = 0, w = z:
a) the surfaces r = const, e = const, z = const form a triply orthogonal family, and
a(x, y, z)
J =
a(r, 0, z)
=r;
b) the element of are length is given by
ds² = dr² + r²d0² + dz?;
c) the components of a vector p are given by
P, = Px cos0+py sin 0, po = -Px sin 0 + Py cos 0, P: = Pzi
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
