International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 319179, 18 pages
doi:10.1155/2009/319179
Chaotic behavior of the biharmonic dynamics system
Vladimir S. Aslanov
Theoretical Mechanics Department, Faculty of Aircraft Construction, Samara State Aerospace University (SSAU), 34 Moscovskoe shosse, 443086 Samara, Russia
Abstract
Motion of a biharmonic system under action of small periodic force and small damped force is studied. The biharmonic oscillator is a physical system acting under a biharmonic force like asinθ+bsin2θ. The article contains biharmonic oscillator analysis, phase space research, and analytic solutions for separatrixes. The biharmonic oscillator performs chaotic motion near separatrixes under small perturbations. Melnikov method gives analytical criterion for heteroclinic chaos in terms of system parameters. A transition from chaotic to regular motion of the biharmonic oscillator was found as the heteroclinic chaos can be removed by increasing the coefficient of a damping force. The analytical results obtained using Melnikov method have been confirmed by a good match with numeric research.