A revisited and general Kane’s formulation applied to very flexible multibody spacecraft

Abstract. Current space missions require predicting the spacecraft dynamics with considerable reliability. Among the various components of a spacecraft, subsystems like payload, structures, and power depend heavily on the dynamic behavior of the satellite during its operational life. Therefore, to ensure that the results obtained through numerical simulations correspond to the actual behavior, an accurate dynamical model must be developed. In this context, an implementation of Kane’s method is presented to derive the dynamical equations of a spacecraft composed of both rigid and flexible bodies connected via joints in tree topology. Starting from the kinematics of two generic interconnected bodies, a systematic approach is derived and the recursive structure of the equations is investigated. The Kane’s formulation allows a relatively simple derivation of the equation of motion while obtaining the minimum set of differential equations, which implies lower computational time. On the other hand, this formulation excludes reaction forces and torques from the dynamical equations. Nevertheless, in this work a strategy to compute them a posteriori without further numerical integrations is presented. Flexibility is introduced through the standard modal decomposition technique, so that modal shapes obtained by FEA software can be directly utilized to characterize the elastic motion of the flexible bodies. A spacecraft composed of a rigid bus and several flexible appendages is modeled and numerical simulations point out that this systematic method is very effective for this illustrative example.