A direct analysis and control of nonlinear time-variant spacecraft dynamics in the vicinity of small irregularly shaped bodies

Development of comprehensive analytical models that describe motion in the vicinity of small irregularly shaped bodies is faced with numerous inimitable challenges. Key among these challenges include uncertainties in the total mass and orbital parameters; irregularities in shape and gravitational potential, etc. Additionally, the ensuing dynamical models tend to be time-varying, parametrically excited nonlinear systems with external periodic excitations. The analysis and control of such nonlinear systems is not a trivial task. Traditionally, techniques applied to study such dynamics tend to be restricted to minimally excited systems or confined to small domains about the operating point. Therefore, by implementing a multi-faceted methodology that relies on Floquet theory, invariant center manifold reduction and normal forms simplification; this research overcomes these limitations and further obtains more accurate closed-form analytical solutions in a lucid and broadly applicable manner. The formulated approach is applied in the analysis and control of motion in the vicinity of asteroid Toutatis. Motion control regimes applied on the realized–more tractable analytical models, show that nonlinear control strategies stabilize the intricate, unwieldy astrodynamics to facilitate scientific missions in the vicinity of Toutatis.