Spin-orbit coupling: A unified theory of orbital and rotational resonances |
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| Authors: | Patrick J Hamill Leon Blitzer |
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| Institution: | (1) Dept. of Physics, University of Arizona, 85721 Tucson, Ariz., U.S.A.;(2) Present address: Dept. of Physics, Clark College, 30314 Atlanta, Ga., U.S.A. |
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| Abstract: | The dynamics of the spin-orbit interaction of a sphereM
8
and a rotating asymmetrical rigid bodyM
a
are examined. No restrictions are imposed on the masses, on the orientation of the rotation axis to the orbit plane, or on the orbit eccentricity. The zonal potential harmonics ofM
a
induce a precession of the spin axis as well as a precession of the orbit plane, the net effect being a uniform precession of the node on an invariant plane normal to the constant total angular momentum of the system. In general, the effect of the tesseral harmonics is to induce short-period perturbations of small amplitude in both the orbital and spin motions. Resonances are shown to exist whenever the orbital and rotational periods are commensurable. In any resonant state a single coordinate is found to represent both orbital and spin perturbations; and the system may be described as trapped in a localized potential well. The resultant spin and orbit librations are in phase with a common period. The relative amplitudes of the spin/orbit modes are determined by the characteristic parameter  =M
a
M
s
a
2
/3(M
a
+M
s
)C, wherea is the semimajor axis of the orbit, andC is the moment of inertia ofM
a
about the rotation axis. When ga 1, the solutions reduce to those for pureorbital resonance, in whichM
s
librates in an appropriate reference frame while the rotation rate of the asymmetrical body remains constant. In the opposite extreme of  1, the solutions are appropriate to purerotational resonance, in which the orbital motion is unperturbed but the spin ofM
a
librates. In each of these special cases the equations developed herein on the basis of a single theory are in agreement with those previously determined from separate theories of spin and orbital resonances. |
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