From the reviews: "The book deals with the geometric theory of mathematical modeling, analysis, and control of 'simple' mechanical systems ... . The text is written with great care and lucidity, includes many exercises, and has clearly benefited from being used in various undergraduate and graduate courses. The book will certainly become a main reference in this area ... ." (A. J. van der Schaft, Mathematical Reviews, 2005h) "Those who are interested in robotic mechanical systems will almost certainly enjoy reading this book. ... intended to be used both as a textbook for graduate students, and at the same time as background material for researchers active in the field of geometric control theory or geometric mechanics. ... authors provide an efficient geometric model for modeling mechanical control systems is brilliant. Precisely this fact makes this book very pleasant to read. In my opinion, it will become a standard reference work in the subject." (Bavo Langerock, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)

• Part I: Modeling of mechanical systems; Introductory examples and problems; Linear and multilinear algebra; Differential geometry; Simple mechanical control systems; Lie groups, systems on groups, and symmetries.- Part II: Analysis of mechanical control systems; Stability; Controllability; Low-order controllability and kinematic reduction ; Perturbation analysis.- Part III: A sampling of design methodologies; Linear and nonlinear potential shaping for stabilization; Stabilization and tracking for fully actuated systems; Stabilization and tracking using oscillatory controls; Motion planning for underactuated systems; Appendices; Time-dependent vector fields; Some proofs.

From the reviews: "The book deals with the geometric theory of mathematical modeling, analysis, and control of 'simple' mechanical systems ... . The text is written with great care and lucidity, includes many exercises, and has clearly benefited from being used in various undergraduate and graduate courses. The book will certainly become a main reference in this area ... ." (A. J. van der Schaft, Mathematical Reviews, 2005h) "Those who are interested in robotic mechanical systems will almost certainly enjoy reading this book. ... intended to be used both as a textbook for graduate students, and at the same time as background material for researchers active in the field of geometric control theory or geometric mechanics. ... authors provide an efficient geometric model for modeling mechanical control systems is brilliant. Precisely this fact makes this book very pleasant to read. In my opinion, it will become a standard reference work in the subject." (Bavo Langerock, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)

• Part I: Modeling of mechanical systems; Introductory examples and problems; Linear and multilinear algebra; Differential geometry; Simple mechanical control systems; Lie groups, systems on groups, and symmetries.- Part II: Analysis of mechanical control systems; Stability; Controllability; Low-order controllability and kinematic reduction ; Perturbation analysis.- Part III: A sampling of design methodologies; Linear and nonlinear potential shaping for stabilization; Stabilization and tracking for fully actuated systems; Stabilization and tracking using oscillatory controls; Motion planning for underactuated systems; Appendices; Time-dependent vector fields; Some proofs.