 00494 Celletti, A., Falcolini, C.
 Normal form invariants around spinorbit periodic orbits
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Dec 10, 00

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Abstract. We consider a model of spinorbit interaction,
describing the motion of an oblate satellite rotating about an internal
spinaxis and orbiting about a central planet. The resulting second order
differential equation depends upon the parameters provided by the
equatorial oblateness of the satellite and its orbital eccentricity.
Normal form transformations around the main spinorbit resonances are
carried out explicitely. As an outcome, one can compute some invariants;
the fact that these quantities are not identically zero is a necessary
condition to prove the existence of nearby periodic orbits (Birkhoff fixed
point theorem). Moreover, the nonvanishing of the invariants provides also
the stability of the spinorbit resonances, since it guarantees the
existence of invariant curves surrounding the periodic orbit.
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