Asymptotic stability of spin orbit resonance for the dynamics of a viscoelastic satellite

Details Asymptotic stability of spin orbit resonance for the dynamics of a viscoelastic satellite Asymptotic stability of spin orbit resonance for the dynamics of a viscoelastic satellite

2010-12-22

arxiv.org/abs/1012.4974v1

Physics

Mathematical Physics

Scientific paper

We prove the asymptotic stability of 1:1 spin orbit resonance for a stiff viscoelastic rotationally invariant satellite. The main point is that we do not assume any dissipation on the orbital degrees of freedom and we prove that anyway they relax to those of a circular orbit, due to the friction acting on the internal degrees of freedom of the satellite. Technically the result is obtained by using the principal moments of inertia as coordinates in the space of elastic configurations and in proving the asymptotic stability through LaSalle's principle, using the energy as a Lyapunov function.

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