Thermally induced attitude dynamics of a spacecraft with a flexible appendage

The performance of a significant number of spacecraft has been impacted negatively by attitude disturbances resulting from thermally induced deformations of flexible appendages. Motions of flexible appendages such as deployable booms and solar arrays result in disturbance torques reacting on the main body of a spacecraft and may have a significant effect on the attitude dynamics and control of the vehicle. The effects of thermally induced structural disturbances of a flexible appendage on the attitude dynamics of a simple spacecraft are investigated. The governing equations, including transient thermal effects, are formulated using a generalized form of Lagrange's equations for hybrid coordinate dynamical systems. An approximate solution based on modal expansion is presented for the case of a step change in solar heating that simulates an orbital eclipse transition. Analytical models are presented for the thermal-structural response of two types of flexible appendages: a thin-walled boom with tip mass and a solar panel. Numerical results demonstrate that the attitude response of the system consists of a slowly developing pointing error and superimposed oscillations whose magnitude is related to the ratio of the thermal and structural response times of the flexible appendage.