Recently, Google, Amazon and others are attempting to develop delivery drones for commercial use, in particular Amazon Prime Air promising 30 minute delivery. One type of commonly used drone proposed for such purposes is a quadcopter. Quadcopters have been around for some time with original development in the 1920’s. They are popular now because they are mechanically simple and provide a good vehicle for unmanned flight. By controlling the speed of the four propellers, a quadcopter can roll, change pitch, change yaw, and accelerate. This research will focus on the study of classical mechanics theories on rigid body motion using the modern mathematical formulation which is based on Lie Group Theory and Differential Topology (abstract manifolds). The goal of this research is to develop a mathematical model for kinematics and dynamics of a quadcopter, and the algorithms for trajectory control.
Huang, Qikai (Bruce Wingo), "Mathematical Modeling of Quadcopter Dynamics" (2016). Mathematical Sciences Technical Reports (MSTR). 158.