3D motion of rigid bodies. A foundation for robot dynamics analysis (Q1755515)

As a whole this book is a useful text for an advanced course on the dynamic modelling of multi-body mechanical systems, and provides readers a more clear understanding in the area of robots modeling and control. Robots can be viewed as a set of multiple rigid bodies, which are controlled to perform complex motions. They present a wide variety of devices: from simple manipulators till complex humanoids, family of robots consisting of one single rigid body that moves in the Euclidean space, such as aircrafts, submarines, and land or surface vehicles. All these are navigation robots -- freely moving 3D objects or they are constraint to move on a 2D space. The Lagrangian formulation is well suited to multi-body systems, butit is very complex for modeling of a single rigid body. However, the numerical methods rely on the physics of the single rigid bodies, whose dynamic is built on the base of the Newton-Euler equations in any of their forms. This is the motivation of the author to offer in the book a simple way of expressing a single dynamic equation for the motion of single rigid bodies, either free motion (6-dimension), such as that of any free space navigation robot or constrained motion (less than 6-dimension), such as that of ground or surface vehicles. In the process, the book also explains the equivalences of (and differences between) the different (Lagrangian and Newton-Euler) formulations. The main content is divided into three parts and eight chapters: Part 1 -- Fundamentals (Ch.1--Ch.2 with mathematical foundations of matrices, linear operators and 3D vector analysis, and the classical mechanics -- Newton's and Lagrange). Part 2 -- Free Motion of Single Rigid Body (Ch.3--Ch.7 containing describing of a rigid motion, attitude representation, dynamics of rigid body, spatial vectors approach, Lagrangian formulation). Part 3 -- Constraint Motion of a Single Rigid Body (Ch.8 treats model reduction under motion constraints). The book ends with four Appendices presenting important details from the text. The book contains a nice nomenclature, a list of figures, a list of tables, but does not contain a Bibliography! After reading this book the reader will be convinced that it is huge research area and the intended audience consisting of mechanical and control researchers and engineers or graduate and PhD students in in the classical mechanics, robotics and mechatronics will find enough material that can be of some help in their independent studies.