Periodic solutions induced by an upright position of small oscillations of a sleeping symmetrical gyrostat

The aim of this paper is to provide sufficient conditions for the existence of periodic solutions emerging from an upright position of small oscillations of a sleeping symmetrical gyrostat with equations of motion [Equation not available: see fulltext.] being α and β parameters satisfying Δ=α 2-4β>0 and β-α2/2 ± α√Δ/2<0, ε a small parameter and, F 1 and F 2 smooth periodic maps in the variable t in resonance p:q with some of the periodic solutions of the system for ε=0, where p and q are positive integers relatively prime. The main tool used is the averaging theory. © 2013 Springer Science+Business Media Dordrecht.