Slew maneuver dynamics of the Spacecraft Control Laboratory experiment

Mathematical expressions for slew maneuver dynamics are presented. The total kinetic energy expression of the system is given as T = T(0) + T(1) + T(2), where T(0), T(1), and T(2) refer to the kinetic energies of the shuttle, the flexible beam, and the tip mass (the reflector), respectively. The specific equations for each of these are defined and integrated into the total energy expression. Using the chain rule in the Lagrange equations and an expression allowing the transformation of the orbiter angular velocity from the inertial frame to the body-fixed frame, the rotational equations are obtained. Finally, the vibration equations for the beam are derived, again using the Lagrange equations.