Stability analysis of a rotating rigid body: The role of external and gyroscopic torques with energy dissipation

Abstract

This is a new study that examines how a rigid body (RGB) reacts to the influence of constant body-fixed torques and gyrostatic torques (GT), as well as the impact of energy dissipation. The RGB’s model being studied includes a spherical slug near the center of mass covered by a viscid layer. Understanding the behavior of this model can offer insights into how RGBs respond to external torques, aiding in the development of more efficient and stable systems for aerospace and robotics applications. The research delves into the relationship between energy dissipation and the GT on the RGB’s motion in three different scenarios involving constant torques around various axes. Detailed analysis, as well as novel simulated results, is presented for different energy dissipation possibilities, such as equilibrium manifolds, periodic or non-periodic solutions, and separatrix surfaces. These new findings are crucial for comprehending, maintaining, and controlling the motion of rigid celestial bodies influenced by external forces in space. The study promises to have a significant impact on the aerospace industry, particularly in the design and operation of spaceships, spacecraft, and satellites, by enhancing our knowledge of rotational motion and celestial bodies’ behavior. A comprehensive report will be produced to elucidate the complexities of rotational and orbital motion discovered during this research.