1 Introduction.- 1.1 Motivation.- 1.2 Outline of the book.- 1.2.1 Energy-based control approaches for several underactuated mechanical systems.- 1.2.2 The hovercraft model, the PVTOL aircraft and the helicopter.- 2 Theoretical preliminaries.- 2.1 Lyapunov stability.- 2.2 Lyapunov direct method.- 2.3 Passivity and dissipativity.- 2.4 Stabilization.- 2.5 Non-holonomic systems.- 2.6 Underactuated systems.- 2.7 Homoclinic orbit.- 3 The cart-pole system.-...