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.
This paper presents a canonical Hamiltonian model of liquid sloshing for the container coupled with spacecraft.Elliptical shape of rigid body is considered as spacecraft structure. Hamiltonian system is an important form of mechanical system.It mostly used to stabilize the potential shaping of dynamical system.Free surface movement of liquid inside the container is called sloshing.If there is uncontrolled resonance between the motion of tank and liquid-frequency inside the tank then such sloshing can be a reason of attitude disturbance or structural damage of spacecraft.Equivalent mechanical model of simple pendulum or mass attached with spring for sloshing is used by many researchers.Mass attached with spring is used as an equivalent model of sloshing to derive the mathematical equations in terms of Hamiltonian model.Analytical method of Lyapunov function with Casimir energy function is used to find the stability for spacecraft dynamics. Vertical axial rotation is taken as the major axial steady rotation for the moving rigid body.
Motion stability of a spacecraft is discussed.A canonical Hamiltonian model for liquid sloshing is presented for a moving rigid body.An equivalent mechanical pendulum model is used to represent the fuel slosh inside the container.In this model sloshing is represented by the moving mass,the rest of the mass of the spacecraft is assumed to be stationary.The spacecraft structure is considered to be an elliptical rigid shape and the steady rotation along the x-axis is taken as the major-axis rotation.Motion stability for the present model is analyzed using the Lyapunov theory with Casimir energy functions.Conditions for stability and instability are derived for a steady principal axis rotation of the rigid body.Simulation results are presented to distribute the region into stable and unstable regions.Besides this,the nonlinear behavior of the system is analyzed under the influence of an external force acting periodically.Chaos is observed through a bifurcation diagram.The time history map and phase portrait are also presented to analyze the nonlinear behavior of the system.
