Data di Pubblicazione:
2015
Citazione:
Asymptotic Behavior of an Elastic Satellite with Internal Friction / E. Haus, D. Bambusi. - In: MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY. - ISSN 1385-0172. - 18:1(2015), pp. 14.1-14.18. [10.1007/s11040-015-9184-7]
Abstract:
We study the dynamics of an elastic body whose shape and position evolve due to the gravitational forces exerted by a pointlike planet. The main result is that, if all the deformations of the satellite dissipate some energy, then under a suitable nondegeneracy condition there are only three possible outcomes for the dynamics: (i) the orbit of the satellite is unbounded, (ii) the satellite falls on the planet, (iii) the satellite is captured in synchronous resonance i.e. its orbit is asymptotic to a motion in which the barycenter moves on a circular orbit, and the satellite moves rigidly, always showing the same face to the planet. The result is obtained by making use of LaSalle’s invariance principle and by a careful kinematic analysis showing that energy stops dissipating only on synchronous orbits. We also use in quite an extensive way the fact that conservative elastodynamics is a Hamiltonian system invariant under the action of the rotation group.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Dynamics of an elastic satellite; La Salle principle; Spin orbit resonance; Mathematical Physics; Geometry and Topology
Elenco autori:
E. Haus, D. Bambusi
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