Scale factors in spherical coordinates

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The discussion focuses on the derivation of scale factors in spherical coordinates, specifically how the value for the scale factors h is determined. The scale factors are essential for converting between Cartesian and spherical coordinate systems, impacting calculations in various fields such as physics and engineering. The document referenced provides a detailed explanation of the mathematical relationships involved in this conversion. Key points include the significance of the radial distance, polar angle, and azimuthal angle in defining these scale factors. Understanding these scale factors is crucial for accurate modeling and analysis in three-dimensional space.
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how they get that result
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how they got that value for the scale factors h?
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Thread 'Help needed with Elliptic Integrals'

I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW
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