Seminario delle Meccaniche

Pseudo-synchronous solutions for dissipative non-autonomus systems

by Guido Gentile (Università degli studi "Roma Tre")


We consider a class of systems on the one-dimensional torus, subject to a periodic perturbation and in the presence of dissipation, and show that, however small the dissipation, if the perturbation is a trigonometric polynomial in the angles and the unperturbed frequencies satisfy a non-resonance condition of finite order, depending on the size of the dissipation, then a quasi-periodic solution persists.  A physically relevant case, where the result applies, is the spin-orbit model, which describes the rotation of a satellite around its own axis, while revolving on a Keplerian orbit around a planet, in the case in which the dissipation is taken into account through the MacDonald torque.

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Giovanni Gallavotti