IGPP Seminar Series

Rotational Kinematics, Cassini States of Solar System Objects, and Stability of Spin

by William I. Newman
Departments of Earth and Space Sciences, Physics and Astronomy, and Mathematics, UCLA

Abstract

We review the Euler equations of rotational motion for bodies responding to a torque, and derive the average of associated potential energy of highly asymmetric ("triaxial") objects undergoing both rotation and revolution. We provide an approximate dynamical description of the long-term behavior of planet-satellite systems emerging from time-averaged equations including both the precession of the spin axis of the satellite and the precession of the satellite's orbit plane around the planet, paying particular attention to departures from axisymmetry in the satellite. We demonstrate the existence of two conservation laws in these circumstances, analogous to rigid body rotation, and derive a one degree of freedom of Hamiltonian to describe this motion. We explore the topology of this Hamiltonian as a function of the underlying physical parameters and the emergence of a bifurcation in the number and character of its stationary solutions, commonly called ``Cassini states.'' Unlike the Euler rigid body problem whose kinematics are describable by the intersection of a sphere with an ellipsoid, the time-averaged dynamics of planet-satellite systems is governed by the intersection of a sphere with a parabolic cylinder. We explore how the interplay of geometrical and dynamical aspects govern the kinematics and stability of such solar system environments, and implications to the physical and compositional evolution of these environments.
Tuesday, 01 June 2010
3853 Slichter Hall
Refreshments at 3:45 PM
Lecture at 4:00 PM