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.
Use of chaotic dynamics for the analysis of tether system motion
This final chapter is devoted to research into the chaotic motion of space tether systems. The Melnikov method and Poincare sections are described briefly. It is shown that the presence of an eccentricity at a system’s orbit leads to chaotisation of motion. For the biharmonic oscillator equation, which describes the motion of a spacecraft with an elastic tether, the analytical solutions for homoclinic and heteroclinic orbits are found. For some particle cases, the analytical representation of the Melnikov function is obtained. The motion of a spacecraft with a vertical elastic tether is investigated by means of the chaotic method, and the conditions for prevention of chaotic motions are found.
On the calculation of turbulent heat transport downstream from an abrupt pipe expansion
A numerical study is reported of flow and heat transfer in the separated flow region created by an abrupt pipe expansion. Computations have employed an adaptation of the TEACH-2E computer program with the standard k ˜ e model of turbulence. The study has given its main attention to the simulation, from both a physical and a numerical viewpoint, of the region in the immediate vicinity, of the wall where turbulent transport gives way to molecular conduction and diffusion. As in other separated flow studies, wall resistance laws or “wall functions” used to bridge this near-wall region are based on the idea that, beyond the viscous sublayer, the turbulent length scale is universal, increasing linearly with distance from the wall. Attention to detailed modeling, however, has, it appears, produced a more satisfactory set of relations than have formerly been used. Predictions of the experimental data of Zemanick and Dougall for a diameter ratio of 0.54 show generally encouraging agreement with experiment. At a d...