# differential equations – Tennis Racket theorem

Torque-free Euler equations experiment seen in low gravity of Russian spacecraft is modelled here with a view to see its tumbling motion around the intermediate axis $$omega_2$$ rotation. However its reversal is not observed here. The boundary conditions do play a role, varying them did not much change the sine behaviour towards interfering periodic flips.

Due to easy demonstration possibility here I posted this hopefully interesting problem although strictly it is a physics problem.

``````{I1, I2, I3} = {8, 4, 0.4};
Dzhanibekov = {I1 TH1''(t) == (I2 - I3) TH2'(t) TH3'(t),
I2 TH2''(t) == (I3 - I1) TH3'(t) TH1'(t),
I3 TH3''(t) == (I1 - I2) TH1'(t) TH2'(t), TH1'(0) == -0.4,
TH2'(0) == 0.08, TH3'(0) == 0.65, TH1(0) == 0.75, TH2(0) == -0.85,
TH3(0) == 0.2};
NDSolve(Dzhanibekov, {TH1, TH2, TH3}, {t, 0, 15.});
{th1(u_), th2(u_), th3(u_)} = {TH1(u), TH2(u), TH3(u)} /. First(%);
Plot(Tooltip({th1'(t), th2'(t), th3'(t)}), {t, 0, 15},
GridLines -> Automatic)
``````

Please help choose better initial conditions for getting a jump around $$theta_2$$ axis. Thanks in advance.

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