Mathematical Engineering

This book provides a solid foundation to the exciting world of aerial autonomy, with a focus on their rigid-body dynamics, sensing and state estimation, and low-level stabilization. It discusses low-speed, propeller-driven flight typical of Uncrewed Aerial Systems. A tensor approach to 3D modelling allows for a very general modelling approach, which is then also translated into easy-to-use equations (e.g., for coding a state estimator). Stability theory and simple control approaches are developed from first principles, and again applied to, and illustrated with, examples in flight. Concepts central to the practising aerospace engineer, such as rotation formalisms (rotation matrix, quaternions) and the dynamics of rotation are treated in depth. The book is aimed at those interested in aerial autonomy or robotics and requires only fundamental mathematical background in linear algebra and differential equations. Problems are provided throughout the text to evaluate knowledge.