DOI: 10.70650/rvimj.2026v3i1007

  DOI URL: https://doi.org/10.70650/rvimj.2026v3i1007

Abstract: The paper investigates the stability of steady motions of a gravitating gyrostat interacting with a spheroidal rigid body under mutual Newtonian attraction. The gyrostat is modeled as a rigid body containing an internal rotor with constant spin, while the spheroid represents an axially symmetric mass distribution generating a central gravitational field with quadrupole effects. Using the equations of motion derived from the Hamiltonian formulation of rigid body dynamics, we characterize relative equilibria corresponding to steady translational–rotational motions, including uniform rotations and circular orbital configurations. The stability analysis is carried out by applying the energy momentum method and Lyapunov’s direct method, supplemented by linearization around equilibrium solutions. Conditions for nonlinear and linear stability are obtained in terms of physical parameters such as the gyrostatic moment, mass distribution, oblateness of the spheroid, and orbital angular velocity. Special attention is given to the influence of the internal rotor on the stabilization or destabilization of steady motions. It is shown that gyrostatic effects can significantly enlarge the domain of stability and, in certain regimes, compensate for destabilizing gravitational gradients produced by the spheroidal field. Several limiting cases are discussed, including the reduction to a classical rigid body without internal rotors and the motion in a purely central gravitational field. The results provide a unified framework for understanding the coupled translational and rotational dynamics of gyrostatic systems in non-spherical gravitational environments. These findings are relevant to applications in astrodynamics and spacecraft attitude dynamics, particularly for satellites equipped with control moment gyros or reaction wheels operating near oblate celestial bodies.

Keywords: Gravitating gyrostat; spheroid; steady motion; relative equilibrium; stability analysis; rigid body dynamics; energy momentum method.