Can Dust Particles Alter the Dynamics of Planar Rotations in Space?

[codex34]

I've been looking at planar rotations, in a volumetric medium, for a while and came up with a rather strange solution I'd like you to take a look at.
Taking a planar rotation where the tangential velocity at n is greater than the tangential velocity at n+1, you always get a singularity at r=0. Not to mention violating c.
If I apply dust to the planar rotation, the dust is drawn towards the center, at the center the maths always blows up to infinity, so no matter what you do you always end up with a planar rotation that fails at r=0.
So I ignored r=0, am I allowed to do that?
Basically I placed a dust particulate at r=0, ignoring the singularity.
With nowhere else to go the dust is squeezed out of the plane by the force of the dust around it, it is ejected either out of the top or bottom of the planar rotation, irregular shaped dust.
So from there I developed a rather strange mechanism, that I have tried to animate.
Please take a look HERE (sorry if the gif is a bit big.)
After looking at the 'model' for a bit I realized the singularity was no longer applicable, it had been replaced with a volume within which the path of a dust particulate changes direction, the problems with r=0 in the planar rotation no longer exist.
Volume of indeterminate dust paths

It looks very nearly like the crab nebula.
crab animation
crab close up image

The really weird thing is that when the dust is stopped, when it's consumed, the two rotating toroids in the animation close up, the resulting shape is almost perfectly spherical, like the sun, but with a similar mechanism in the middle.

I've seen the shapes this mechanism produces a lot in astronomy, and it's sending me loopy in the head, am I seeing that mechanism (whatever it is) in everything, or am I just projecting something I've conjured up?

 

[AndyW]

Thank you for sharing your findings and thoughts on planar rotations. I find your ideas very interesting and would be happy to discuss them further.

Firstly, let's address your question about ignoring the singularity at r=0. While it may seem convenient to simply ignore this point, it is not a valid approach in scientific research. Singularities are important indicators of where a theory or model may break down and should not be disregarded.

In your case, it seems that the introduction of dust in the planar rotation has caused the singularity to no longer be applicable. This could be due to the dust particles altering the dynamics of the system, making it more complex and potentially creating new equilibrium points. It would be worthwhile to investigate this further and see if there are any mathematical explanations for the changes in the system.

Your animation and images of the resulting shapes are indeed interesting and resemble the crab nebula. However, it is important to note that while there may be similarities, it does not necessarily mean that your mechanism is the same as the one responsible for the formation of the nebula. It would require extensive research and evidence to make such a claim.

I encourage you to continue exploring and developing your ideas, but also to approach them with a critical and scientific mindset. Perhaps seeking out collaborations with other scientists who specialize in this field could also help validate your findings.

Thank you for sharing your work and I wish you all the best in your research.