Dynamics of a gyrostat on cylindrical and inclined Eulerian equilibria in the three-body problem

Periodic solutions induced by an upright position of small oscillations of a sleeping symmetrical gyrostat

“…These rotors may rotate with respect to the platform in such a way that the mass distribution within the system as a whole is not altered; this will produce an internal angular momentum, designated as gyrostat momentum, which will be normally regarded as a constant. Note that when this constant vector is zero, the motion of the system is reduced to the motion of a rigid solid, see for instance Figure 1 where a gyrostat in the frame of the three body problem is presented, and [3,4] or [5] for more details on this class of mechanical systems. The objective of this paper is to provide, using the averaging theory, a system of nonlinear equations whose simple zeros provide periodic solutions of the differential system (1).…”

Stabilizing the coupled orbit–attitude dynamics of a rigid body in a J2 gravity field using Hamiltonian structure

“…When the gravitationally coupled orbit-attitude dynamics model of a rigid body in a J 2 gravity field is adopted in the future asteroid mission design, the relative equilibrium of the rigid body can be used as the nominal motion, which has also been shown by other studies in the three body problem [14,4,5]. Then, the stabilization of relative equilibria is necessary during the mission, since the stability of relative equilibria of uncontrolled system cannot be always guaranteed by the parameters of spacecraft.…”

Dynamics of a gyrostat satellite with the vector of gyrostatic moment tangent to the orbital plane

“…Wang and Xu (2012) studied the relative equilibria of a rigid body, using geometric mechanics, when considering the J2 perturbations of an oblate gravitational field. Guirao and Vera (2010) analysed a gyrostat dynamics in the frame of the three-body problem using geometrical and mechanics methods to describe the Eulerian equilibria and to study their bifurcation, while Vera (2009) employed the same non-canonical Hamiltonian dynamics approach to the three-body problem for a triaxial gyrostat. Ousaloo (2016) developed a control scheme to overcome the nutation motion of an asymmetric satellite, independent of its inertia, by adding an axial reaction wheel on the desired spin axis.…”