We consider dissipative one-dimensional systems subject to a periodic force. As a model system, particularly suited for numerical analysis, we investigate the driven cubic oscillator in the presence of friction, and study numerically how time-varying friction affects the dynamics. We find that, if the damping coefficient increases in time up to a final constant value, then the basins of attraction of the leading resonances are larger than they would have been if the coefficient had been fixed at that value since the beginning. From a quantitative point of view, the scenario depends both on the final value and the growth rate of the damping coefficient. The relevance of the results for the spin-orbit model is argued and discussed in some detail.
Bartuccelli, M., Deane, J., Gentile, G. (2012). Attractiveness of periodic orbits in parametrically forced systems with time-increasing friction. JOURNAL OF MATHEMATICAL PHYSICS, 53(10), 102703-1-102703-27 [10.1063/1.4757650].
Attractiveness of periodic orbits in parametrically forced systems with time-increasing friction
GENTILE, Guido
2012-01-01
Abstract
We consider dissipative one-dimensional systems subject to a periodic force. As a model system, particularly suited for numerical analysis, we investigate the driven cubic oscillator in the presence of friction, and study numerically how time-varying friction affects the dynamics. We find that, if the damping coefficient increases in time up to a final constant value, then the basins of attraction of the leading resonances are larger than they would have been if the coefficient had been fixed at that value since the beginning. From a quantitative point of view, the scenario depends both on the final value and the growth rate of the damping coefficient. The relevance of the results for the spin-orbit model is argued and discussed in some detail.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
