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Vrbic

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I know how to solve "typical" Kepler problem but I'm interested in a global view to "binary" systems. For example Earth - Moon. If I set lagrangian of system as ##L=\frac{1}{2}(m_1\dot{r}_1^2 + m_2\dot{r}_2^2)-V(|r_2-r_1|)## there isn't included a spin.

My questions are:

1) If it is solved as two body (I guess, two points) problem. Is possible to put there a term describing a spin?

2) Why the spin isn't in general solution of Kepler problem?

3) Whether it is possible. How? What term could describe the spins? ##L_s=\frac{1}{2}(J_1\dot{\phi}_1^2 + J_2\dot{\phi}_2^2)##? ; J - moment inertia

4) Anyway, if or not would be possible to create lagrangian with spin. Does it change some characteristic of motion? (shape of orbit, period, etc.)?

Thank you for your replies.

My questions are:

1) If it is solved as two body (I guess, two points) problem. Is possible to put there a term describing a spin?

2) Why the spin isn't in general solution of Kepler problem?

3) Whether it is possible. How? What term could describe the spins? ##L_s=\frac{1}{2}(J_1\dot{\phi}_1^2 + J_2\dot{\phi}_2^2)##? ; J - moment inertia

4) Anyway, if or not would be possible to create lagrangian with spin. Does it change some characteristic of motion? (shape of orbit, period, etc.)?

Thank you for your replies.

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