Control of Underactuated Mechanical Systems: Stabilisation and Limit Cycle Generation clearly and simply explains the concepts of stabilization and stable limit cycle generation for the class of Underactuated Mechanical systems. It demonstrates all the proposed concepts through real-time experiments on a real UMS subject and explores the challenges and constraints related to real-time control design. These concepts are illustrated in terms of the modeling and control of systems, such as the inertia wheel inverted pendulum (IWIP). This book is organized into three parts: Part I: General context and case study; Part II: Control solutions for the stabilization problem; Part III: Control solutions for stable limit cycle generation In the first part of this book, the images and diagrams clearly introduce the reader to the concept of stabilization and limit cycle generation. The focus then progresses to the proposed system as a case study; namely the inertia wheel inverted pendulum, including its description, mathematical modeling, and experimental setup. The second part is devoted to the problem of stabilization; where control solutions are presented and discussed, as well as their implementation issues and validation through numerical simulations and real-time experiments. The final part addresses the problem of stable limit cycle generation, where the proposed control solution is detailed, as well as its related issues of implementation and validation through different case studies. This book serves as a valuable resource for PhD and Master students, engineers, researchers, and teachers. Its content guides them in the field of robotics and automatic control, with a simplified methodology to control dynamical underactuated mechanical systems.