Bifurcation analysis of attitude dynamics in rigid spacecraft with switching control logics

A numerical continuation method is used for bifurcation analysis of the complex behavior that appears in the attitude dynamics of rigid spacecraft as a result of switching logics in control system elements. Because the stability analysisoflimitcyclesiscarriedoutinmostcircumstances,theapplicationofthecontinuationmethodraisesanum- berofissueswhensuchaspectsasnonlinearitiesthatcannotbeapproximatedbydifferentiablefunctionsandnonin- vertibleinput–outputrelationsaretakenintoconsideration.Anapproachbasedonthecontinuationofequilibrium points of the Poincare ́ map for the analysis of dynamic systems with motion-dependent discontinuities is presented. Spacecraft con gurations featuring single-axis control loops are investigated, where momentum wheels or reaction thrusters are used. In the latter case, the characterization of the dynamic behavior of a pulse-modulated control system is used as an example of the proposed methodology. The results show that the considered con gurations can be successfully analyzed by the continuation technique, without performing extensive numerical simulation.