I will present a new dynamic extension of the thrust variable in the quadcopter dynamics that preserves the positive sign of the thrust. This extension not only eliminates the positive sign constraint on the thrust variable, but also leads to feedback linearization of the quadcopter dynamics. For the latter, an atlas is constructed on the entire state space of the quadcopter so that the quadcopter is transformed to a 14-dimensional linear controllable system on each chart in the atlas. Based on the chart-wise dynamic feedback linearization of the quadcopter, a global tracking strategy is proposed and its excellence is demonstrated with a simulation study.