| Abstract | This paper aims to explore the rotatory spatial motion of an asymmetric rigid body (RB) under torques which is fixed inside the RB (CBFTs) with nonzero first component of a gyrostatic moment vector (GM). Euler's equations of motion are employed to deduce a series of dimensionless equations of motion (EOM). These equations are subsequently introduced for the assessment of stability at equilibrium points (EPs). Specifically, this study develops 3D phase space trajectories for three distinct scenarios; two of them are applied constant torques that are directed on the minor and major axes, while the third one is the action of applied constant torque on the body’s middle axis. Novel analytical and simulation results for both scenarios of constant torque applied along the minor and middle axes are provided in the context of separatrix surfaces (SS), equilibrium manifolds, periodic or non-periodic solutions, and periodic solutions’ extreme. Concerning the situation of a directed torque on the major axis, a numerical solution for the problem is presented in addition to a simulation of the graphed results for the angular velocities' trajectories in various regions. Moreover, the influence of GM is examined for each case and a full modeling for the body's stability has been presented. The exceptional impact of these results is evident in the development and assessment of systems involving asymmetric RBs, such as satellites and spacecraft. It may serve as a motivating factor to explore different angles within the GM in similar cases, thereby influencing various industries, including engineering and astrophysics applications. |