On the coupled dynamics of small spacecraft and elastic deployable appendages

A thorough investigation of the dynamics of finite-mass satellites with a deployable elastic arm is presented. This work is focused on the interaction between spacecraft rigid body motion and its flexible arm dynamics during the deployment process. The classical Newton–Euler formulation and the Lagrangian approach are applied to the study of the dynamics of spacecraft and its deploying arm. Utilizing a non-Newtonian floating frame to define the arm elastic deformation field, the interactions between the spacecraft and its moving arm have been simulated. Complete equations of motion show that the spacecraft motion induces dynamical stiffness on the arm; in addition, axial and lateral motions of the deploying elastic arm change the spacecraft mass-characteristics and thus influence the spacecraft’s rigid body motions. The overall dynamic behavior is highly dependent on spacecraft mass characteristics in addition to the “arm deployment time (ADT)”. The results of case studies clearly indicate that some assumptions previously applied in appendage dynamic analysis are not conservative and produce erroneous results. This study realistically investigates the dynamics of elastic deploying appendages by considering finite-mass characteristics for small and massy spacecraft. The results reveal that for massive spacecraft the arm’s flexible dynamics is mainly excited through deployment, while for small spacecraft the energy transfers to the arm base and the spacecraft rigid body motion is considerably stimulated. Moreover, this work has further highlighted the effects of ADT in the overall system response. The findings of this work show that the energy distribution between arm’s elastic dynamics and spacecraft rigid body motions is an important factor in the design of any control system to limit unwanted arm-tip motions.