(2): Consider the curvilinear coordinate system defined by 2 X = uj-12, y = 2 u, u2, z = u3 Show that the system is orthogonal and right handed. Compute the scale factors (ii) Find V. A and Vx. for the vector field A u, e,+u, e2+u, e; %3D (iii) Find the expression for V´w (u,,u2, u3).
(2): Consider the curvilinear coordinate system defined by 2 X = uj-12, y = 2 u, u2, z = u3 Show that the system is orthogonal and right handed. Compute the scale factors (ii) Find V. A and Vx. for the vector field A u, e,+u, e2+u, e; %3D (iii) Find the expression for V´w (u,,u2, u3).
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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Pic 1:Q1
Pic:Q2
![PROBLEM (2):
Consider the curvilinear coordinate system defined by
2.
y =
2 u, u2,
Z = u3
(i)
Show that the system is orthogonal and right handed. Compute the scale factors.
(ii)
Find V. A and VXA for the vector field A = u, e,+ u, e2+u, es
. 2
(iii)
Find the expression for V´y (u,, u2, u3).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34cc4e3b-a1d0-44cd-9110-a9f4d8aa478b%2F81667a18-bb8c-4c79-803a-9d5b2ef0c542%2Fizq7ot5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:PROBLEM (2):
Consider the curvilinear coordinate system defined by
2.
y =
2 u, u2,
Z = u3
(i)
Show that the system is orthogonal and right handed. Compute the scale factors.
(ii)
Find V. A and VXA for the vector field A = u, e,+ u, e2+u, es
. 2
(iii)
Find the expression for V´y (u,, u2, u3).
![PRO
e point
PROBLEM (8):
In cylinderical polar coordinates, A = r cos 0 er+r sin e e e. Find V. A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34cc4e3b-a1d0-44cd-9110-a9f4d8aa478b%2F81667a18-bb8c-4c79-803a-9d5b2ef0c542%2Fmdll77p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:PRO
e point
PROBLEM (8):
In cylinderical polar coordinates, A = r cos 0 er+r sin e e e. Find V. A.
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