Libration and the Nature of Cassini States: Steady Co-precession of Spin and Orbit Poles

Details Libration and the Nature of Cassini States: Steady Co-precession of Spin and Orbit Poles Libration and the Nature of Cassini States: Steady Co-precession of Spin and Orbit Poles

May 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009dda....40.1404n&link_type=abstract

American Astronomical Society, DDA meeting #40, #14.04; Bulletin of the American Astronomical Society, Vol. 41, p.908

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Libration in the moon and other planets and satellites can be defined, after clarifying underlying geometrical issues, as a set of ordinary differential equations analogous to those for a spinning rigid body. We show the emergence of two conservation laws, and how one of these can be converted formally into a Hamiltonian whose dynamics explicitly reduce to a quadrature. The stationary solutions of this Hamiltonian are the so-called Cassini states and describes the steady co-precession of spin and orbit poles. The topology of the Hamiltonian and its dependence upon the defining physical parameters identifies the number of such states. We show how the position and number of Cassini states varies as a function of the parameters including how the emergence of two new states depends in a particularly sensitive way on the physical parameters. In addition, we provide a new geometrical approach to the traditional parabola-meets-unit circle configuration and a new methodology for obtaining the homoclinic orbit that it defines. We then relate this comprehensive development of the dynamics to the moon and other celestial bodies, and speculate on the role of dissipative and other processes on these states.

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