Advanced Dynamics

Abstract

7R7. Advanced Dynamics. - RB Bhat (Concordia Univ, Montreal, Canada) and RV Dukkipati (Sch of Eng, Fairfield Univ, Fairfield CT 06430-5195). Narosa Publ, New Delhi, India. Distributed in USA by CRC Press LLC, Boca Raton FL. 2001. 395 pp. ISBN 0-8493-1018-0. $99.95.Reviewed by M Pascal (Lab de Modelisation en Mec, Univ Pierre et Marie Curie, Tour 66, 4 Place Jussieu, Paris, 75252 Cedex 05, France).The authors’ aim is to provide a textbook giving insight about the methods used in Analytical Mechanics and which are related to abstract concepts like generalized parameters, virtual displacements, and variational principles. In contrast with other textbooks, the authors did not assume that the basic knowledge of kinematics and dynamics is familiar to the reader; the transition to this abstract presentation of the fundamental laws of mechanics is performed very gradually. The result is a book involving altogether topics related to elementary backgrounds (suitable for first-year graduate students) about dynamics of particles and rigid bodies and advanced theoretical part (useful for undergraduate senior students). The book involves 12 chapters, each of them is followed by a list of references and a great amount of homework problems. The fundamental laws of Mechanics are presented in the first chapter. Only systems of particles or plane motions of rigid bodies are considered in this chapter. Several topics (kinematics of rigid bodies, radius of gyration, center of percussion…) are introduced, but some other basic concepts like Galileen frame, relative and absolute velocities, Coriolis acceleration…are missing and will be presented only in Chapter 4. This reviewer is not convinced that this first chapter is very suitable. For first level students, a more detailed presentation is needed, and for senior students, all these concepts are known. Chapter 2 deals with more interesting topics such as generalized coordinates, classification of constraints, virtual works principle, and generalized forces. However, in this part, only systems of particles are considered, and the fundamental distinction between external and internal forces is not underlined. Several elementary concepts are presented in Chapters 3 and 4, like potential and kinetics energies, linear and angular momentum vectors, relative motions, and transformation of coordinates systems. The Foucault’s pendulum gives an interesting example of these topics. In Chapter 5, an introduction to Kepler’s laws and to orbital motion is presented. Chapter 6 deals with Lagrange equations for holonomic and non-holonomic systems. First integrals are introduced for systems with cyclic coordinates. A great amount of examples are solved. The next two chapters are devoted to basic knowledges about inertia tensors, principal axes of inertia and dynamics of rigid bodies. As an example, the motion of the spinning top is solved. Chapter 9 presents variational methods. Hamilton’s and the least action principle are derived, together with Hamilton’s equations. Canonical transformations and Hamilton-Jacobi equations are studied in Chapter 10; Lagrange and Poisson brackets are also introduced.An interesting classification of dynamics systems is given at the beginning of Chapter 11, devoted to vibrations. Then the linear vibrations of single-degree-of-freedom systems are investigated. The forced vibrations are also considered for harmonic and arbitrary excitation forces. For multi-degree-of-freedom systems, usual modal analysis is presented for undamped and damped cases. The last chapter provides an introduction to numerical methods. Several explicit and implicit numerical schemes are presented for the integration of linear dynamical systems. An example of a non-linear system is then solved by means of these numerical methods in order to underline the problems encountered in this case. In conclusion, this reviewer thinks that this book is without doubt very useful at a time when many students, and even many scientists, think that Analytical Mechanics belongs to the past. Several interesting examples of the use of these methods may be found in this book. In spite of rather numerous printing mistakes in the text, the book is clearly written with a lot of good quality figures. This reviewer thinks that Advanced Dynamics can be used by senior students and also scientists involved in systems dynamics and interested in analytical methods rather than numerical methods.