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.
In this paper, the chaotic dynamics in an attitude transition maneuver of a slosh-spacecraft coupled with flexible appendage in going from minor axis to major axis spin under the influence of dissipative effects due to fuel slosh and a small flexible appendage constrained to only torsional vibration is investigated. The slosh-spacecraft coupled with flexible appendage in attitude maneuver carrying a sloshing liquid is considered as multi-body system with the sloshing motion modeled as a spherical pendulum. The focus in this paper is that the dynamics of the liquid and flexible appendage vibration are coupled. The equations of motion are derived and transformed into a form suitable for the application of Melnikov’s method. Melnikov’s integral is used to predict the transversal intersections of the stable and unstable manifolds for the perturbed system. An analytical criterion for chaotic motion is derived in terms of system parameters. This criterion is evaluated for its significance to the design of spacecraft. The dependence of the onset of chaos on quantities such as body shape and magnitude of damping values, fuel fraction and torsional vibration frequency of flexible appendage are investigated. In addition, we show that a spacecraft carrying a sloshing liquid, after passive reorientation maneuver, will end up with periodic limit motion other than a final major axis spin because of the intrinsic non-linearity of fuel slosh. Furthermore, an extensive numerical simulation is carried out to validate the Melnikov’s analytical result.
