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.
Resonance at motion of a body in the Mars's atmosphere under biharmonical moment
An uncontrolled motion of a reentry vehicles in the rarefied Mars's atmosphere is investigated. Such reentry vehicle has small lengthening and a blunted form for effective braking [1]. This type of Lander can have three balancing positions of a spatial angle of attack: α*=0, α*=≠0, α*=π depending on the position of the center mass. The change of a dynamic pressure the descent into the atmosphere can lead to resonance. It is shown, that the numerical integration of motion equations does not give reliable results due to the probabilistic character of transients with related to resonance. The conditions of movement stability are received identified for various areas of movement under resonance. The suggestion is to calculate the top and bottom parameters of movement using averaged equations. The research shows that the resonance could cause the accident the Beagle 2 Lander.
Thermally Induced Dynamics of Satellite Solar Panels
Thermally induced structural motions are known to affect the attitude dynamics of low Earth orbiting satellites during eclipse transitions. Motions of e exible appendages such as solar panels lead to rigid body rotations of the entire satellite because the total angular momentum of the system is conserved. These potentially large attitude disturbances may violate pointing accuracy and jitter requirements. One type of thermally induced dynamics exhibited by solar panels is thermal snap. The Upper Atmosphere Research Satellite is a prominent example of a satellite that experiences thermal snap disturbances during eclipse transitions. This paper describes recent studies of thermally induced dynamicsof solarpanels, including an analysisofsatelliteattitudedynamics resulting from thermally induced structural motions and a laboratory investigation of the thermal-structural performance of a satellite solar panel. Analytical and experimental results demonstrate thermal bending deformations with acceleration transients that have characteristic thermal snap disturbance histories in response to rapid changes in heating. The studies show that solar panel thermal snap disturbances are caused by through-the-thickness temperature differences that vary at a nonconstant rate. Finite element analysis correctly predicts the thermal snap phenomenon observed in the solar panel experiments.