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In this article, using finite element method the effects of the preload on the nonlinear dynamic behavior of the noncircular two lobe aerodynamic journal bearing have been investigated. Assuming that the rotor is solid, the governing Rynolds equations for both the gas lubricant and rotor equation of motion in static and dynamic conditions have been derived and performance of the noncircular aerodynamic journal bearing in different conditions has been evaluated. Rung Kutta method has been used to solve the time dependent equations of motions of noncircular aerodynamic journal bearing and its gas lubricant. Using the numerical results, to investigate the motion of the center of the rotor in dynamic conditions, the graphs of frequency response, power spectrum, dynamic trajectory, Poincare map and bifurcation diagram have been plotted. The results show periodic, quasi periodic and chaotic rotor behavior for different bearing preload. It is concluded that appropriate selection of rotor parameters like its preload and suitable design and fabrication of rotor and its bearing can prevent any undesirable perturbed motions of the shaft and both the collision and wear of the rotor and bearing.

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In this paper, we investigate chaos in attitude dynamics of a rigid satellite in an elliptic orbit analytically and numerically. The goal in the analytical part is to prove the existence of chaos and then to find a relation for the width of chaotic layers based on the parameters of the system. The numerical part is aimed at validating the analytical method using the Poincare maps and the plots obtained on the sensitivity to initial conditions. For this end, first, the Hamiltonian for the unperturbed system is derived. This Hamiltonian has three degrees of freedom due to the three-axis free rotation of the satellite. However, the unperturbed attitude dynamics has two first-integrals of motion, namely, the energy and the angular momentum. Next, we use the Serret-Andoyer transformation and reduce the unperturbed system Hamiltonian to one-degree of freedom. Then, the gravity gradient perturbation due to moving in an elliptic orbit is approximated in Serret-Andoyer variables and time. Due to this approximation and simplification, the system Hamiltonian transforms to a one-degree-of-freedom non-autonomous one. After that, Melnikov’s method is used to prove the existence of chaos around the heteroclinic orbits of the system. Finally, a relation for calculating the width of chaotic layers around the heteroclinic orbits in the Poincare map of the Serret-Andoyer variables is analytically derived. Results show that the analytical method gives a good approximation of the width of chaotic layers. Moreover, the results show that the analytical method is accurate even for orbits with large eccentricities.