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 attitudedynamics and reorientation maneuver for completely vis-cous liquid-filled spacecraft with flexible appendage.All ofthe equations of motion are derived by using Lagrangianmechanics and then transformed into a form consisting of anunperturbed part plus perturbed terms so that the system'snonlinear characteristics can be exploited in phase space.Emphases are laid on the chaotic attitude dynamics producedfrom certain sets of physical parameter values of the space-craft when energy dissipation acts to derive the body fromminor to major axis spin.Numerical solutions of these equa-tions show that the attitude dynamics of liquid-filled flexiblespacecraft possesses characteristics common to random,non-periodic solutions and chaos,and it is demonstrated that thedesired reorientation maneuver is guaranteed by using a pairof thruster impulses.The control strategy for reorientationmaneuver is designed and the numerical simulation resultsare presented for both the uncontrolled and controlled spinstransition.
B. Yue Department of Mechanics, School of Science,Beijing Institute of Technology, 100081 Beijing, China
