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.