This paper addresses the problem of performing quadrotor aggressive maneuvers that are attitude-constrained. The trajectory generation is formulated as a quadratic programming problem with linear constraints. Constraints at a specific time can be imposed on any linear combination of the quadrotor position and its derivatives. The under-actuation of the vehicle is explored to embed the attitude constraints into the trajectory generation via constraints on the desired quadrotor acceleration. A trajectory tracking controller is also proposed that guarantees the asymptotic stability of the closed-loop tracking system. Experimental and simulation results illustrate the application of the proposed method to quadrotor maneuvers involving a 360° flip.