To search for volume elements at a specific coordinate, such as volume elements at a specific coordinate. ball coordinates (r, 0, ¢ ), we can lower their shape by reference from coordinates others, such as cartesian coordinates (x, y, z), using relationships dt cartesian = det)dtnew With J is a Jacobian matrix measuring 3 x 3. Suppose a new coordinate is notated as (X, Y, Z), then dTparu dXdYdZ and удх дх дху ax əY az ду ду ду J = ax əY az az az az ax ay əz Determine the Jacobian matrix J and the volume element of the ball coordinates! (x =r sin 8 cos o, y =r sin e sin o, z = r cos 0)
To search for volume elements at a specific coordinate, such as volume elements at a specific coordinate. ball coordinates (r, 0, ¢ ), we can lower their shape by reference from coordinates others, such as cartesian coordinates (x, y, z), using relationships dt cartesian = det)dtnew With J is a Jacobian matrix measuring 3 x 3. Suppose a new coordinate is notated as (X, Y, Z), then dTparu dXdYdZ and удх дх дху ax əY az ду ду ду J = ax əY az az az az ax ay əz Determine the Jacobian matrix J and the volume element of the ball coordinates! (x =r sin 8 cos o, y =r sin e sin o, z = r cos 0)
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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Transcribed Image Text:To search for volume elements at a specific coordinate, such as volume elements at a specific
coordinate. ball coordinates (r, 0, o ), we can lower their shape by reference from coordinates
others, such as cartesian coordinates (x, y, z), using relationships
dt cartesian = det(J)dtnew
With J is a Jacobian matrix measuring 3 x 3. Suppose a new coordinate is notated as (X, Y, Z), then
dtbaru = dXdYdZ and
дх дх дх-
ax əY az
ду ду ду
J =
ax aY az
az əz
az
ax əY az
Determine the Jacobian matrix J and the volume element of the ball coordinates!
(x =r sin e cos p, y =r sin e sin o, z =r cos 0)
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