Find the expression of the metric ds? = (dx')? + (dx²)² + (dx³)² and it's 1st and 2nd components of fundamental tensor in cylindrical coordinates (x x' = x' cos x? x2 = x' sin x? x3 = x3 %3D %3D where x' are Cartesian coordinate system.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find the expression of the metric ds² = (dx')² + (dx²)² + (dx³)²
and it's 1st and 2nd components of fundamental tensor in cylindrical coordinates (x')
x' = x' cos x²
x2
= x' sin x?
x3 = x3
where x' are Cartesian coordinate system.
Transcribed Image Text:Find the expression of the metric ds² = (dx')² + (dx²)² + (dx³)² and it's 1st and 2nd components of fundamental tensor in cylindrical coordinates (x') x' = x' cos x² x2 = x' sin x? x3 = x3 where x' are Cartesian coordinate system.
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