Nonlinear dynamical behavior of a three-degree-of-freedom asymmetric rigid body under gyroscopic torque

The study in this paper focuses on solving the problem of rigid body (RB) rotary motion under the effect of both gyrostatic torque (GT) and the body’s constant fixed torques (BCFTs). The controlling equations of motion (EOMs), in such a case, are derived from Euler’s kinematic equations. Novel analytical solutions for the body angular velocities are approached in three instances: major, minor, and intermediate with a detailed description of the stability regions, equilibrium points (EPs), and the motion critical points. The extreme value of the case is also examined, with stabilization addressed in two sections. Each section offers a solution and includes a table of extreme values within the stable separatrix region. Additionally, the effect of distinct GT values on the motion’s paths and stabilization is analyzed, resulting in valuable insights for this scenario. For each case, a comprehensive estimation of the maximum values and minimum ones at distinct non-dimensional angular velocity components (NAVCs) in addition to periodic solutions has been approached. A contour mapping for the motion is presented to see the influence of the GT on the separatrix surfaces (SS), non-periodic or periodic solutions, and extreme periodic ones. Moreover, a three-dimensional (3D) representation of the numerical solution in the intermediate case was presented to also reveal the GT impact. The significant implications of these findings are clear in systems’ designing and evaluation utilizing asymmetric RBs, such as spaceships. This research could inspire further exploration of different perspectives within the GT in comparable scenarios, potentially impacting numerous fields, such as the engineering industry and navigation.