The generalized method of phase trajectory curvature synthesis in spacecraft attitude dynamics tasks

The attitude dynamics of a variable mass spacecraft is considered. The variability of mass-inertia parameters in time is associated with operation of a jet-engine, which forms an interorbital impulse. The thrust of the jet-engine is directed along the longitudinal spacecraft axis, which fulfills the nutational-precessional motion relative to a planned direction in the inertial space. Therefore, to increase an accuracy of the thrust impulse formation during the jet-rocket engine work, and to reduce dispersion of the thrust due to the precessional rotation, it is needed to synthesize the motion regime with monotonously decreasing nutation angle. Such regimes allow to obtain a spiral twisting of the longitudinal axis to the predefined target direction, when the thrust will be focusing to target direction. To analyze and to synthesize this nutational-precessional motion properties, the curvature of the corresponded phase trajectories is evaluated in an angular phase space. The phase trajectory curvature evaluation gives an opportunity to synthesize the appropriate time-dependencies of inertia-mass parameters of spacecraft, which allows to increase the accuracy of the thrust impulse formation during operation of the jet-rocket engine. The proposed appropriate technique for positive phase trajectory synthesis is based on the previously developed method of curvature evaluation. •The attitude dynamics of a variable mass spacecraft was considered.•The general case of the mathematical model of the angular motion of the rigid body of variable mass was developed.•The qualitative method of phase trajectories curvature synthesis for non-autonomous dynamical systems was generalized.•The qualitative analysis of the attitude dynamics of the variable mass spacecraft was fulfilled.