Abstract
AbstractIn 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.
Highlights
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
The review work of Chai [37], in which authors have discussed path planning and controllability of spacecraft models using different techniques in detail, has motivated us to work on the design of controller for bringing stability in sloshing effect which arises inside coupled tank and leads to havoc in dynamics of gyrostat
Normal form theory was utilized to show oscillatory solutions in mechanical model coupled with fuel filled tank
Summary
Abstract: 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. The same biological model is analysed in the presence of fear effect [12] for the existence of oscillatory solutions, whereas two different food chain models are considered by Sahoo and Samanta in their work [13], with the effect of delay parameter, to investigate switching of stability through Hopf bifurcation. We have noticed that several biological models are taken into account for oscillatory solutions [35,36] in the aforementioned citations, but impact of seeking local oscillatory solutions using Andronov–Hopf bifurcation for spacecraft with attached fuel tank is never discussed. The review work of Chai [37], in which authors have discussed path planning and controllability of spacecraft models using different techniques in detail, has motivated us to work on the design of controller for bringing stability in sloshing effect which arises inside coupled tank and leads to havoc in dynamics of gyrostat.
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