Chaotic Behavior of the Biharmonic Dynamics System
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 . 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.
Oscillations of a Spacecraft with a Vertical Elastic Tether
The motion about a center of mass of a spacecraft with a vertical elastic tethered system under the action of the gravitational moment and small periodic tethered force at a circular orbit is studied. The mathematical model is derived using Lagrange’s equations including tether vibrations and oscillations of the spacecraft relatively to the proper mass center. The paper contains bifurcation analysis, phase space study, and analytic solutions for separatrixes. The considered mechanical system performs chaotic motion near separatrixes under the influence of small disturbances. The Melnikov method gives a criterion for homo/heteroclinic chaos in terms of system parameters. Results of the study can be useful for the analysis of gravitational stabilization systems with space tethers and for studying the behavior of a spacecraft with a deployed tether.
Investigations of dielectric gratings using electrodynamic models based on volume integral equations
Eigenmodes of planar and cylindrical dielectric gratings (DGs) and electromagnetic wave scattering from multiplayer DGs are investigated. The DG characteristics are calculated using numerical-analytical solution of integral equations (IEs).