Chaotic behavior and detailed parameter analysis of stretch-twist-fold (STF) flow are investigated. STF flow is associated with fluid particle motion which naturally arises in the dynamo theory. It proposes a mechanism, by which a celestial bodies, such as earth and sun, can maintain and amplify the magnetic field continuously. Parameter analysis is performed using linearization theory for different choices of parameters. The existence of Heteroclinic trajectory of Sil'nikov type is proved using an undetermined coefficient method. It connects two non trivial equilibrium points. As a consequence, the Sil'nikov criterion guarantees that STF flow has Smale horseshoes chaos.
The present paper investigates the chaotic attitude dynamics and reorientation maneuver for completely viscous liquid-filled spacecraft with flexible appendage. All of the equations of motion are derived by using Lagrangian mechanics and then transformed into a form consisting of an unperturbed part plus perturbed terms so that the system＇s nonlinear characteristics can be exploited in phase space. Emphases are laid on the chaotic attitude dynamics produced from certain sets of physical parameter values of the spacecraft when energy dissipation acts to derive the body from minor to major axis spin. Numerical solutions of these equations show that the attitude dynamics of liquid-filled flexible spacecraft possesses characteristics common to random, non- periodic solutions and chaos, and it is demonstrated that the desired reorientation maneuver is guaranteed by using a pair of thruster impulses. The control strategy for reorientation maneuver is designed and the numerical simulation results are presented for both the uncontrolled and controlled spins transition.
B. Yue Department of Mechanics, School of Science,Beijing Institute of Technology, 100081 Beijing, China
