×

Periodic and homoclinic motions in forced, coupled oscillators. (English) Zbl 0959.70015

The author studies periodic and homoclinic motions in periodically forced, weakly coupled oscillators in the form of perturbations of two independent planar Hamiltonian systems. The subharmonic Melnikov method is extended, and existence, stability and bifurcation theorems for periodic orbits are given. These theory is applied to weakly coupled Duffing oscillators. Particular attention is devoted to the system \(\dot q_1=p_1\), \(\dot p_1=q_1- q_1^3+ \varepsilon (-\delta p_1- \beta q_1q^2_2+ \gamma\cos \omega t)\), \(\dot q_2=p_2\), \(\dot p_2=q_2-q^3_2+ \varepsilon (-\delta p_2-\beta q^2_1q_2)\), where \(\delta,\beta, \gamma\) and \(\omega\) are positive constants. A large variety of situations is studied and discussed depending on the above parameters.
Reviewer: S.Nocilla (Torino)

MSC:

70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics
70K40 Forced motions for nonlinear problems in mechanics
37N05 Dynamical systems in classical and celestial mechanics
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
PDFBibTeX XMLCite
Full Text: DOI