A triple definite integral from Cartesian coordinates to Spherical coordinates. Help! 3.

2020年2月15日 · Now consider the conversion from cartesian to spherical coordinates described here (after the line "The conversion of a direction to spherical angles can be found by ..."). They use the $\operatorname{atan2}$ function to obtain $\phi$ via $\phi=\operatorname{atan2}(y,x)$. Why is this correct even when $\sin\theta=0$? Am I missing something or ...

2020年12月1日 · The spherical basis for tensors has little to do with spherical coordinates in anything but name, and merits its own question. It is useful for QM-laddering of states along the z-axis, and is an efficient complex structure summarily handling x …

James and my answers have the same understanding of what spherical coordinates are for a point, but we invented two different definitions for spherical coordinates of a vector. My definition is: place the vector's starting point at the origin and …

In fact, $ x=r\cos\theta\sin\phi $, $ y=r\sin\theta\sin\phi $ and $ z=r\cos\phi $ were actually used in deriving the expressions for transformation from spherical to cartesian by considering the case of r=1 or in our notations $ \rho=1 $ within the three dimensions of a …

2017年10月11日 · If you follow the link from that page to the main article on spherical coordinates, in particular, to the Cartesian Coordinates section of that article, you will find the following caveat: The inverse tangent denoted in $\varphi = \arctan\frac yx$ must be suitably defined, taking into account the correct quadrant of $(x,y)$.

I can partially answer this. I believe your first matrix is not the correct general transformation matrix for cartesian to spherical coordinates because you are missing factors of $\rho$ (the radial coordinate), as well as some other incorrect pieces. So it is not clear what you are trying to show.

2017年8月31日 · Cartesian, spherical and cylindrical coordinates [closed] Ask Question Asked 7 years, 3 months ago. ...

2021年4月14日 · Conversion from Cartesian to spherical coordinates, calculation of volume by triple integration. 3.

Rotations in spherical coordinates are affine transformations so there isn't a matrix to represent this on the standard basis $(\theta,\phi)$, you'll need to introduce another coefficient here: $(\theta,\phi,1)$, the rotation matrix in the $\theta$ direction is …