Hopf bifurcation analysis for liquid-filled Gyrostat chaotic system and design of a novel technique to control slosh in spacecrafts

In this article, a fuel tank is coupled with gyrostat in a moving spacecraft to discuss its dynamical behaviour and bringing stability in velocity vectors. Parametric study is performed using Hopf bifurcation to find the bifurcation parameter for a considered mechanical model. Furthermore, a region is constructed in which negligible limit cycles appear around unstable spirals for angular momentum greater than bifurcation point. Based on local dynamical analysis, trajectories of angular velocities are observed with respect to damping constant, which is formulated in the form of bifurcation parameter. Moreover, a controller is designed in this article for considered dynamical system by achieving global stability, with the help of Lyapunov theory, into the spacecraft coupled with filled fuel tank, and their results are compared with effective spacecraft control strategies to observe the effectiveness of our proposed control technique. Finally, in presented research, numerical simulations are performed using MATLAB for validation of analytical results, which the authors have achieved for Hopf bifurcation and designed controller.