Relaxation Oscillations in Tidally Evolving Satellites

Details Relaxation Oscillations in Tidally Evolving Satellites Relaxation Oscillations in Tidally Evolving Satellites

Feb 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997cemda..67..111q&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 67, Issue 2, pp.111-130

Astronomy and Astrophysics

Astronomy

2

Tidal Despinning, Limit Cycles, Cassini States, Relaxation Oscillations, Singular Perturbations, Singular Perturbations.

Scientific paper

We study the rotational evolution under tidal torques of axisymmetric natural satellites in inclined, precessing orbits. In the spin- and orbit-averaged equations of motion, we find that a global limit cycle exists for parameter values near the stability limit of Cassini state S_1 . The limit cycle involves an alternation between states of near-synchronous spin at low obliquity, and strongly subsynchronous spin at an obliquity near 90°. This dynamical feature is characterized as a relaxation oscillation, arising as the system slowly traverses two saddle-node bifurcations in a reduced system. This slow timescale is controlled by ɛ, the nondimensional tidal dissipation rate. Unfortunately, a straightforward expansion of the governing equations for small ɛ is shown to be insufficient for understanding the underlying structure of the system. Rather, the dynamical equations of motion possess a singular term, multiplied by ɛ, which vanishes in the unperturbed system. We thus provide a demonstration that a dissipatively perturbed conservative system can behave qualitatively differently from the unperturbed system.

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