RK1

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I am trying to make a very rough animation of a rotating pulsar magnetosphere that would very roughly resemble this gif.
I was able to make a sphere and the dipolar field lines. I was wondering if anyone could provide any possible suggestion regarding.

1. How do i animate the rotation such that the rotation axis is not z but slightly misaligned to z.

2. Is there a better way to make the field likes from the poles (jets).

restart

[1.1, cos(theta), theta]

[1.1, cos(theta), theta]

(1)

sph := [.5, theta, phi]; c1 := [A*sin(phi)^2, 0, phi]; c2 := [A*sin(phi)^2, (1/6)*Pi, phi]; c3 := [A*sin(phi)^2, (1/3)*Pi, phi]; c4 := [A*sin(phi)^2, (1/2)*Pi, phi]; c5 := [A*sin(phi)^2, 2*Pi*(1/3), phi]; c6 := [A*sin(phi)^2, 5*Pi*(1/6), phi]

[A*sin(phi)^2, (5/6)*Pi, phi]

(2)

NULL

NULL

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A := 2; plot3d([c1, c2, c3, c4, c5, c6, sph], phi = 0 .. 2*Pi, theta = 0 .. 2*Pi, coords = spherical, plotlist = true, scaling = constrained)

2

 

 

NULL

s1 := [sqrt(theta), 1, 1/10]; s2 := [sqrt(theta), 3, -1/10]; s3 := [sqrt(theta), 2, 1/10]; s4 := [sqrt(theta), 1.7, 1/7]

p := plot3d([sph, s1, s2, s3, s4, s5, s6, c1, c2, c3, c4, c5, c6], phi = 0 .. 2*Pi, theta = 0 .. Pi, coords = spherical, orientation = [-75, 58, 10], scaling = constrained, color = ["SkyBlue", "yellow", "yellow", "yellow", "yellow", "yellow", "yellow", "red", "red", "red", "red", "red", "red"])

``

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plots[animate](plot3d, [[sph, s1, s2, s3, s4, s5, s6, c1, c2, c3, c4, c5, c6], theta = 0 .. Pi, phi = 0 .. 2*Pi, orientation = [B, 45, 52], coords = spherical], B = -180 .. 180)

NULL

 

Download Pulsar_temp.mw

3. Any other suggestions that could help with the aesthetics.

Is there a way to suppress dependencies of a all functions appearing in a worksheet without having to do suppress([each function])?

Is there a way to compute the Riemann tensor for two different metrics in the physics package without each time setting up the metric. For example you just put the metric as an argument to do so in the differential geometry package.

How would I go about creating a tetrad of a specific signature in the Differential Geometry package. The GrahmSchmidt and NullTetrad give me orthonormal and complex null tetrads. But I was wondering if there was a way to generate a tetrad of specific signature.

Is there a way to execute an entire worksheet for a list of values of a parameter.
Sometimes executing in the standard loop can be cumbersome given you have to add catch statements for errors to prevent the loop from stopping.

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