**34th Meeting of the AAS Division on Dynamical Astronomy, May 2003**

* 10 Satellites and Rings*

Oral, Tuesday, May 6, 2003, 3:25-5:10pm,
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## [10.06] New Problems and Theories of Synchronous Rotation

*F. Varadi (UCLA), S. Musotto (UCLA and Univ. of Padova, Italy), W. Moore, G. Schubert (UCLA)*

The dynamics of synchronous rotation and physical librations
are revisited in order to establish a general framework
applicable to a variety of problems. The orientation matrix
of the body is decomposed around the equilibrium state into
perfectly synchronous rotation and deviation. The normal
modes of the linearized equations are computed in the case
of a circular satellite orbit, yielding both the periods and
the eigenspaces of three librations. Libration in longitude
decouples from the other two, vertical modes. First, there
is a fast vertical mode, with a period very close to the
average rotational period. It corresponds to tilting the
body around a horizontal axis while retaining nearly
principal-axis rotation. In the inertial frame, this mode
appears as nutation and free precession. The other, a slow
vertical mode, is the free wobble. The effects of orbital
inclination are investigated from the point of view of
Cassini states. Orbital eccentricity has a surprisingly
large effect on physical librations due to an interaction
between free precession and wobble. A perturbation theory is
outlined to explain the nature of the interaction.

The author(s) of this abstract have provided an email address
for comments about the abstract:
varadi@ucla.edu

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Bulletin of the American Astronomical Society, **35** #4

© 2003. The American Astronomical Soceity.