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How do you derive the differential volume element in spherical coordinates d(tau) from Cartesian?

Posted 26 days ago

Dear Community:

How does one derive the d(tau), which is r^2*[Sin(theta)]d(r)d(theta)d(phi) from d(x)d(y)d(z)?

Thank you,
Patrick Merrill

POSTED BY: Patrick Merrill
3 Replies

Dear Gianluca,

Perfect!

Thank you!!

Patrick Merrill

POSTED BY: Patrick Merrill

Faster:

CoordinateChartData["Spherical",
  "VolumeFactor",
 {r, \[Theta], \[CurlyPhi]}]
POSTED BY: Gianluca Gorni

Here is a way:

D[FromSphericalCoordinates[{r, \[Theta], \[CurlyPhi]}],
   {{r, \[Theta], \[CurlyPhi]}}] // Det // Simplify
POSTED BY: Gianluca Gorni
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