This section describes the various coordinate systems that are used to describe the position of orientation of aircraft, and the transformation between these coordinate systems. It is necessary to use several different coordinate systems for the following reasons: Newton's equations of motion are given the coordinate frame attached to the UAV. Some of the on-board sensors take measurements in the body frame, e.g., rate gyros, while some of the sensors take measurements in the inertial frame, e.g., GPS. Aerodynamics forces and torques are exerted in the body frame. Most system requirements, e.g., flight trajectories, are specified in the inertial frame.