This work addresses the tracking issue for a non-inertial frame referenced quadrotor unmanned aerial vehicle (UAV) controlled by a cascaded proportional-integral-derivative (PID) controller. Some of the current applications of quadrotors, such as those used in sea search and rescue operations, are launched from a moving vessel. The landing of such quadrotors must consider the non-inertial position of the vessel to be landed on. Nearly every study in this area has represented the dynamics of a quadrotor UAV based on a fixed inertial frame. The most widely used inertial frames are the geodetic coordinate system that depends on the Earth's surface and the Earth-centered fixed coordinate system. This work aims to analyze the orientation, rotation, velocity, and position of a quadrotor that is based on a moving object. The quadrotor kinematics will consider the rotation and orientation for both a non-inertial frame of reference (vessel) and a fixed inertial frame of reference (base point). The system dynamics will depend on the initial take-off point as an inertial reference to give the correct dynamical effects on the quadrotor body frame. Most accidents occur during bad weather conditions, in which case, cascaded PID controllers should be used to control a quadcopter to face weather disturbances.