Examples of use of cylindrical coordinates over cartesian coordinates, examples
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You should essentially always use whatever coordinate system makes your equations look simplest. (Sometimes this won’t be obvious.)
The natural way to do this is to note when your problem has some sort of rotational symmetry, and use the appropriate (spherical or cylindrical) coordinate system in that context.
As a rule of thumb:
Rotational symmetry in all three dimensions : spherical coordinates
Rotational symmetry in 2-d, translational symmetry in another: cylindrical
Full translational symmetry: Cartesian
If you only have some of those symmetries, then it probably doesn’t matter - use whatever is convenient. (Typically, I’d default to Cartesian.)
On the other hand, if you have more exotic symmetries, it might be time to start looking into more general coordinate systems, known as curvilinear coordinates.
At the end of the day, though, the only thing that changes between the different coordinate systems is algebra. In one system, you might get a much more complicated expression, but you know it’s still (in principle) just as solvable so long as you can translate between the coordinate systems.
HOPE THIS HELPS YOU!!! ❤❤❤
You should essentially always use whatever coordinate system makes your equations look simplest. (Sometimes this won’t be obvious.)
The natural way to do this is to note when your problem has some sort of rotational symmetry, and use the appropriate (spherical or cylindrical) coordinate system in that context.
As a rule of thumb:
Rotational symmetry in all three dimensions : spherical coordinates
Rotational symmetry in 2-d, translational symmetry in another: cylindrical
Full translational symmetry: Cartesian
If you only have some of those symmetries, then it probably doesn’t matter - use whatever is convenient. (Typically, I’d default to Cartesian.)
On the other hand, if you have more exotic symmetries, it might be time to start looking into more general coordinate systems, known as curvilinear coordinates.
At the end of the day, though, the only thing that changes between the different coordinate systems is algebra. In one system, you might get a much more complicated expression, but you know it’s still (in principle) just as solvable so long as you can translate between the coordinate systems.
HOPE THIS HELPS YOU!!! ❤❤❤
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