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In this paper we present some recent results on the description and control of the attitude motion of rotating rigid bodies. We derive a new class of globally asymptotically stabilizing feedback c o n trol laws for the complete (i.e., dynamics and kinematics) attitude motion. We s h o w that the use of a Lyapunov function which i n volves the sum of a quadratic term in the angular velocities and a logarithmic term in the kinematic parameters leads to the design of linear controllers. We alsodoi:10.2514/3.21698 fatcat:n7o5lut2dbeffburnogkhr4s2q