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) =r; a(r, 0, z) b) the element of are length is given by ds? = dr² +r²d0² + dz?; c) the components of a vector p are given by Pr = Px cos 0 + Py sin 0, Po = -Px sin 0 + Py cos 0, P: = Pz; d) grad U has components: 2U lâu au. e) divp= (rp.) + t); f) curl p has components: ape ap apr ae az az ar ae g) v²u is given by (3.66). v²U = au a2U + əz²
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) =r; a(r, 0, z) b) the element of are length is given by ds? = dr² +r²d0² + dz?; c) the components of a vector p are given by Pr = Px cos 0 + Py sin 0, Po = -Px sin 0 + Py cos 0, P: = Pz; d) grad U has components: 2U lâu au. e) divp= (rp.) + t); f) curl p has components: ape ap apr ae az az ar ae g) v²u is given by (3.66). v²U = au a2U + əz²
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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