How to convert magnus effect from 2d to 3d?

[icandothemath]

I am working on simulating the magnus effect of lift on a spinning ball. Right now spinning on the z axis I can calculate the force effect it has on the x and y coordinates.

If I am to add spin on the x do I do the exact same calculations effecting the y and z coords and just add them to the z spin forces?

And again do the same with the y spin effect on the x and z coords?

Thanks

 

[MarcusAgrippa]

Express the answer you have obtained in coordinate independent form. To do this, interrogate the system by asking what directions does the system itself define. The axes x, y, and z were introduced by you and are not really relevant to the physical system. On the other hand, the unit vector in the direction of the local velocity and in the direction of the spin axis are physically defined directions. Try expressing your result in terms of these.

 

[icandothemath]

Thanks for the reply MarcusAqgrippa. I ended up stumbling upon this article that explains the effect in 3D space. http://www.crm.cat/en/publications/publications/2013/pr1154.pdf I do not totally understand it though. My implementation of the 2D effect can be found here http://forum.unity3d.com/threads/ho...-to-the-3d-world-sample-code-included.321682/ Now I just need a bit of help taking the 3D article and understanding the difference between my 2D model and how to implement that in source code.

 

[MarcusAgrippa]

That is a very nice article. In the theory it does what I suggested that you do, and more: it sets up the equations of motion and produces a solution by perturbation techniques.

You did not say initially that you were trying to construct a numerical model for the 3-d problem. That is a lengthy piece of work, and is not something that I have time to do. If you have well formulated questions, I may be able to assist you in answering them. But I think you may be asking for more.

Perhaps someone else with more time on their hands can assist you. It would nevertheless be useful were you to formulate your current difficulty a little more precisely. Your open ended plea for help may not attract many responses.

 

[icandothemath]

Ok, maybe as I go through that document I can ask for some help if that is ok?
In figure 1 of the pdf document. It talks about unit vector l, v, and v x l. Then spin rates around these axis.
I am unsure what these axis are. The arrows in figure 1 do not make sense to me.
They look like like point arbitrarily in directions. Except for v which looks to line up with the x axis.

Also in the Force equations below it says m is mass but there is no m in the formulas.