On the motion of an oscillator with a periodically time-varying mass

The stability of the motion of an oscillator with a periodically time-varying mass is under consideration. The key idea is that an adequate change of variables leads to a newtonian equation, where classical stability techniques can be applied: Floquet theory for the linear oscillator, KAM method in the nonlinear case. To illustrate this general idea, first we have generalized the results of [W.T. van Horssen, A.K. Abramian, Hartono, On the free vibrations of an oscillator with a periodically time-varying mass, J. Sound Vibration 298 (2006) 1166-1172] to the forced case; second, for a weakly forced Duffing's oscillator with variable mass, the stability in the nonlinear sense is proved by showing that the first twist coefficient is not zero. (C) 2008 Elsevier Ltd. All rights reserved.