Relative equilibria of an intermediary model for the roto-orbital dynamics. The low rotation regime

Abstract

Abstract We address the attitude dynamics of a triaxial rigid body in a circular orbit. This task is done by means of an intermediary model, which is obtained by splitting the Hamiltonian in the form H = H 0 + H 1 , where H 0 is required to be a non-degenerate integrable Hamiltonian system. A numerical study is presented comparing the dynamics of the new intermediary model with the full system (MacCullagh’s truncation) and showing a competitive performance for the cases Sun-asteroid and Earth-spacecraft. This model defines a Poisson flow endowed with invariants defining a S M 2 × S M 2 reduced space. We analyze the coupling between the orbital mean motion and rotational variables. The key role played by the moments of inertia and the value of the angular momentum is shown in detail. The analysis of the intermediary shows that, under slow rotation regime, the classic dynamics of the free rigid body is no longer maintained: bifurcations with changes of stability are displayed for several critical inclinations of the rotational angular momentum plane and for critical orientations of the body frame. Moreover, the evolution of the angular momentum plane is given by a time dependent harmonic oscillator.