**DDA 36th Meeting, 10-14 April 2005**

*Session 4 Dynamics of Rotating Bodies*

Oral, Monday, April 11, 2005, 3:05-5:25pm
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## [4.01] Non-Hamiltonian perturbation theory for deformable fast rotators

*F. Varadi, W. B. Moore (UCLA)*

Deformable fast rotators, such as the Earth and Mars, change
both their rotational states (spin axis direction) and
shapes due to external forces and internal material motions.
The standard approach to rigid-body dynamics is Hamiltonian
perturbation theory in canonical action-angle (Andoyer)
variables which incorporate the moments of inertia form the
outset. Dealing with deformations is usually based on linear
perturbation theory around rigid-body reference solutions
which yields transfer functions from the rigid to the
deformable case. We present the elements of a general,
non-Hamiltonian perturbation theory in non-canonical
variables based on Lie series. First, we present general
results on non-Hamiltonian perturbation theory and
averaging, such as a coordinate-free formula for the
solution of the homological equation of the Lie series in
the case of perturbed periodic orbits. In general, the
averaged system does not fully Lie-commute with the
unperturbed system and the reduction of the averaged system
to the orbit space of unperturbed system has to allow for
drift along the unperturbed orbits. In the case of a fast
rotator, we start with rotation around the spin axis as the
unperturbed system. The orientation of the body is
represented as a rotation matrix and we derive the
appropriate Lie bracket. After averaging over the rotation
period, we reduce the system by eliminating the phase
variable associated with pure rotation around the spin axis.
The reduced system is expressed in terms of the spin axis in
both inertial and body frames. We compare our results to
those of traditional Hamiltonian theories and numerical
simulations. This work is supported by NSF Planetary
Astronomy.

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, **37** #2

© 2005. The American Astronomical Soceity.