Attitude Dynamics: Modeling and Control

In this chapter about attitude dynamics, modeling and control are treated together. After the derivation of the classical Newton's and Euler's equations of rotation, the complete set of the attitude equations, including kinematics and dynamics, is built and employed to design an attitude control law capable of forcing the kinematic variables of a rigid body (angular acceleration, angular rate, and attitude) to track their target trajectories. Stability conditions are found in the continuous and discrete-time domains. Control law design is completed by the design of a state predictor, which aims to predict the state variables of the control law on the basis of different sets of measurements. The design method is typical of EMC, and was already deployed in Chapter 6 . Classical subjects such as the attitude of a torque-free rigid body and the gravity gradient stabilization are treated and completed with the topics of aerodynamic stability “in the small” (around zero attitude equilibrium) and “in the large” (around nonzero attitude equilibriums). The topics have been suggested by the European GOCE mission. Two classical control strategies, which are appropriate of the early phases of a space mission (just after orbit injection), are reviewed. Active nutation control is intimately connected with gyroscopic stability and energy dissipation. Spacecraft detumbling allows us to introduce the angular rate control by means of magnetic torquers and to exploit some theoretical tools from the literature. These tools are partly used in the last section, which is committed to the modeling and control of a spacecraft actuated by reaction wheels and magnetic torquers.