Energy Decay in a Gyrostatically Influenced Rigid Body

The rotational motion of rigid bodies (RBs) subjected to external torques is fundamental to understanding dynamics in various engineering applications. A RB model comprising a spherical slug centered near the RB's center of mass, covered by a viscid layer, provides valuable insights into RB dynamics when exposed to external torques. Analyzing such systems' stability is essential for designing efficient and stable systems in aerospace and robotics, particularly for spacecraft and satellites involving rotor-stabilization, internal moving masses, and fuel sloshing. This study examines the rotational dynamics of a semi-RB under constant body-fixed torques (CBFTs) and a gyrostatic moment (GM), considering internal energy dissipation (ED). The impacts of ED alongside GM on the body's motion are explored in three cases involving constant torque about the major, minor, and intermediate axes. A non-dimensional model is developed, reducing the system's reliance to five fundamental parameters. Linear stability analysis is performed to assess the stability of various equilibrium points (EPs) concerning torques around different principal axes. Extensive numerical simulations are conducted to investigate the global dynamics. For major axis torque, the system settles into a pure spin-up maneuver, with viscosity and GM affecting the transient path and final spin amplitude. For minor axis torque, no EPs exist, and trajectories continuously evolve while crossing separatrices. For intermediate axis torque, motion can remain in certain phase space regions or transition between them, with GM serving as a critical control parameter. Analysis of perturbed motion confirmed linear stability predictions, with trajectories forming stable or unstable oscillations around equilibria. Novel outcomes include equilibrium manifolds, periodic and non-periodic solutions, and separatrix surfaces. These findings directly impact the design and attitude control of aerospace systems, including spacecraft and satellites. The identified stability regions and transition behaviors can inform control law design and maneuver planning for celestial RB motion in space.