Can the Kepler Problem be Solved for Bodies with Spin?

[Vrbic]

Hello I'm wondering, what is difference in trajectory or period or...something if I try to compare solution of Kepler problem for point bodies and "rigid" bodies with spins. More precisely is some easy way how to include a spin of bodies to this problem? Or this procedure for describing of such situation is not valid anymore? If you may let me know some book or some link about that.
Thank you all.

 

[zwierz]

for a simplest example consider a barbell (two equivalent mass points linked by a weightless rod) in the gravity field of a fixed mass point. Consider a planar motion

Actually it is a very hard problem, you can find only partial results in articles, not in textbooks

 

[Vrbic]

for a simplest example consider a barbell (two equivalent mass points linked by a weightless rod) in the gravity field of a fixed mass point. Consider a planar motion

Actually it is a very hard problem, you can find only partial results in articles, not in textbooks

So do you mean I should try to compute a case when a barbell rotate around some central point object? And compare with general solution (without a spin)?
What procedure would you suggest? Using Lagrangian and solve Euler-Lagrange equations? Or how to insert "a spin" into general Kepler problem?

 

[zwierz]

I suggest that you write down the Lagrange equations and solve them numerically to make sure that it is a chaotic system and it does not have any relation to the Kepler problem. Perhaps some hope could be possible if you introduce a small parameter.