anton_dys

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These are questions asked by anton_dys

How come I got this:

as an output of plot(sqrt(Pi/(2*x))*BesselJ(3+1/2, x), x = 0 .. 0.5e-1),

and got this:

for plot(sqrt(Pi/(2*x))*BesselJ(3+.5, x), x = 0 .. 0.5e-1).

Is 1/2 so much different from 0.5 to make Bessel function misbehave at small arguments?? Or is it just a bug?

Hello everyone!

I am confronted with a problem that seems to result from different definition of spherical coordinates in Maple and in Student[VectorCalculus] package.

I want to visualize a vector field defined in spherical coordinates (r,theta,phi).

A simple exampe is < 0, theta, 0 >. If I want to see just one slice of the field in OXY plane, I type:

fieldplot3d(<0, theta, 0>, r = 0 .. 1, theta = 0 .. 2*Pi, phi = 0 .. Pi, coords = spherical, grid = [10, 20, 3], color = black, fieldstrength = fixed(1), arrows = THICK)

And get:

which looks OK more or less but I don't like the nonuniform distribution of arrows. But since the field is defined in spherical coordinates there seems to be no way to produce a uniform distribution with fieldplot3d command.

However VectorField command in Student[VectorCalculus] package seems to do just what I want. But a similar call to it:

SetCoordinates('spherical'[r, theta, phi])

VectorField(<0, theta, 0>, output = plot, view = [-5 .. 5, -5 .. 5, -10 .. 10], fieldoptions = [arrows = THICK, color = black, grid = [10, 10, 3], view = [-5 .. 5, -5 .. 5, -1 .. 1]])  produces quite a different result:

which means that the second argument 'theta' is not the azimuthal angle but the angle from the Z axis, and amounts to Pi/2 since we look at the OXY plane.

The result of: VectorField(<0, 0, theta>, output = plot, view = [-5 .. 5, -5 .. 5, -10 .. 10], fieldoptions = [arrows = THICK, color = black, grid = [10, 10, 3], view = [-5 .. 5, -5 .. 5, -1 .. 1]])  looks better:

but is not correct since the magnitude of the field does not change with the azimutal angle. Finally, 

VectorField(<0, 0, phi>, output = plot, view = [-5 .. 5, -5 .. 5, -10 .. 10], fieldoptions = [arrows = THICK, color = black, grid = [10, 10, 3], view = [-5 .. 5, -5 .. 5, -1 .. 1]]) produces almost what I want:

but it's quite different from what you get with fieldplot3d command. Apparently, not only azimuthal angle is now the third argument but it varies from -Pi to Pi, not from 0 to 2Pi as it does in fieldplot3d. I hoped to use both fieldplot3d and VectorField  with my vector fields but I cannot since they are not consistent in the definition of spherical coordinates.

My questions therefore are:

1) Is there a way to redifine spherical coordinates in VectorField command to make them consistent with the rest of Maple?

2) Can I produce a uniform 3D distribution of arrows for a field in spherical coordinates without VectorField command?

Many thanks for your help in advance!

Hello everyone!

I have a vector field defined in spherical coordinates and I want to plot a sphere colored according to the magnitude of the vector field on that sphere. Is there a simple way to do this?

Many thanks in advance!

 

Hello everyone!

I miss a convinient way to build interactive plots with parameters assigned to sliders. E.g. of such expressions as "a*sin(b*x+c)". Before Maple 2017 I could just right-click the expression, choose "plot builder" and then select "interactive plot with three parameters". That's it. Since the introduction of the new interactive plot builder I am at a loss because that way have been lost and I don't know any other way equally quick and convinient. "Interactive plot builder" now means quite another thing!

Any suggestions?

 

 

Hello everyone!

I am wondering why the Tabulate command does not work with Explore. E.g.:

Explore(`DocumentTools:-Tabulate`([plot(sin(a*x)), plot(cos(x-a))]), parameters = [[a = 0 .. 10, controller = slider]])

I know that I can display an array of plots with the display(Array([....])) which works fine with explore but Tabulate is another good way to display multiple plots and it gives better control over individual plots properties (e.g. setting different size to different plots). Is this a bug or Tabulate is just not meant to work in that context?  

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