This book addresses dynamics modeling and control design methods for nonlinear mechanical systems. The premise of the book is that the two topics are closely related and should be studied together. Most systems of a practical interest are designed to perform various tasks, to work and serve a man. In order to execute work and services, these systems have to be controlled. Tasks and work that are to be completed as well as design and operation conditions are specified by task-based constraints or by other means. We may say, though, that most systems are constrained systems, and referring to nonlinear systems we mean that they are either holonomic or nonholonomic. These are mobile robots and vehicles, aircraft, underactuated manipulators, underwater vessels, space robots, a free-floating astronaut, multifinger grippers, and others. The examples also indicate that many systems are of interest to both mechanics and control. Robotics is an excellent example of a domain where systems are subjected to a variety of constraints, either material or task based. A robotic system can be viewed as a prototype of a system subjected to programmed constraints. Programmed constraints, roughly speaking, are motion specifications put on a system by a design or control engineer to obtain its desired behavior.