Warning, the `spherical` coordinate system was accessed earlier in this session, but its definition changed when loading the Physics package. Consider using the spherical_math or spherical_physics coordinate system.
Description
Examples
See Also
This warning occurs when you have used spherical coordinates and then load the Physics package.
There are two widely used conventions for how to represent spherical coordinates, which in Maple are called spherical_math and spherical_physics. The first is more commonly used in mathematics, and the second in physics. The only difference is a swap between the second and third coordinate.
Spherical coordinates (r,u,v)
in terms of rectangular (Cartesian) coordinates
Rectangular coordinates (x,y,z)
in terms of spherical coordinates
Coordinate system name in Maple
r=x2+y2+z2
tanu=yx
v=arccoszr
x=rcosusinv
y=rsinusinv
z=rcosv
spherical_math
u=arccoszr
tanv=yx
x=rcosvsinu
z=rcosu
spherical_physics
In Maple, the spherical coordinate system can represent either. Loading the Physics package causes Maple to interpret spherical as spherical_physics. When using plotting commands or the changecoords command, you can be specific about which definition to use by giving the option as coords=spherical_math or coords= spherical_physics. For more about the coordinate systems, including the spherical coordinate system, see the coords help page.
Example 1
In Maple, if the Physics package has not been loaded, then in the following plotting command, the spherical_math definition is used.
Here, a partial sphere is plotted using spherical coordinates. In this graph, u measures the angle in the horizontal direction (XY plane), and v measures downward from the positive z-axis to a point. (These are called the azimuthal angle and the polar angle.)
withplots:
plot3d1, u = 0 .. π2, v= 0 .. π, coords = spherical, scaling = constrained
If you load the Physics package after doing a spherical coordinates calculation, you'll get this warning to notify you that a different definition is now being used for spherical coordinates.
withPhysics:
plot3d1, u = 0 .. π2, v= 0 .. π, coords = spherical, scaling = constrained
You can see here that in the second graph, u measures downward from the positive z-axis to a point and v measures the angle in the XY plane.
Solution 1.
You can specify which of these definitions to use. If you want to always use the first, use coords=spherical_math. No warning message is produced.
plot3d1, u = 0 .. π2, v= 0 .. π, coords = spherical_math, scaling = constrained
Solution 2.
Alternatively, if you want the alternate definition, specify it using coords=spherical_physics
plot3d1, u = 0 .. π2, v= 0 .. π, coords = spherical_physics, scaling = constrained
coords, plot3d
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