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.
Chaotic dynamics of an unbalanced gyrostat
Abstract The free three-dimensional motion of an unbalanced gyrostat about the centre of mass is considered. The perturbed Hamiltonian for the case of small dynamical asymmetry of the rotor is written in Andoyer–Deprit canonical variables. The structure of the phase space of the unperturbed system is analysed, six forms of possible phase portraits are identified, and the equations of the phase trajectories are found analytically. Explicit analytical time dependences of the Andoyer–Deprit variables corresponding to heteroclinic orbits are obtained for all the phase portrait forms. The Melnikov function of the perturbed system is written for heteroclinic separatrix orbits using the analytical solutions obtained, and the presence of simple zeros is shown numerically. This provides evidence of intersections of the stable and unstable manifolds of the hyperbolic points and chaotization of the motion. Illustrations of chaotic modes of motion of the unbalanced gyrostat are presented using Poincare sections.
Thermodynamic Evaluation of Solar Integration into a Natural Gas Combined Cycle Power Plant
The term integrated solar combined-cycle (ISCC) has been used to define the combination of solar thermal energy into a natural gas combined-cycle (NGCC) power plant. Based on a detailed thermodynamic cycle model for a reference ISCC plant, the impact of solar addition is thoroughly evaluated for a wide range of input parameters such as solar thermal input and ambient temperature. It is shown that solar hybridization into an NGCC plant may give rise to a substantial benefit from a thermodynamic point of view. The work here also indicates that a significant solar contribution may be achieved in an ISCC plant, thus implying substantial fuel savings and environmental benefits.