The fundamentals of AUV dynamics modeling involve physical principles and mathematical formulations required to describe and predict the AUV’s motion in three-dimensional (3D) space under various operational and environmental conditions. It is divided into kinematics and kinetics. Together, kinematics and kinetics provide a comprehensive framework for modeling AUV motion, capturing both trajectory and the governing forces. Kinematics focuses on the transformation of linear and angular velocities, describing how the position, orientation, and velocity of the vehicle change over time. It deals only geometrical aspects of motion without considering forces, using a three-dimensional coordinate system (e.g., North-East-Down frame) and Euler angles (roll, pitch, yaw) or quaternions for orientation. The AUV’s motion is further described by linear and angular velocities, which are transformed between the body-fixed and earth-fixed reference frames using rotation matrices.