3R12. Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems; for Engineers, Physicists, and Mathematicians. - JG Papastavridis (Georgia Inst of Tech, Atlanta, GA). Oxford UP, New York. 2002. 1392 pp. ISBN 0-19-512697-1. $295.00.
Reviewed by K Yagasaki (Dept of Mech and Syst Eng, Gifu Univ, 1-1 Yanagido, Gifu, 501-1193, Japan).
This big book consisting of about 1400 pages and 174 figures provides comprehensive treatments for constrained systems with finite degrees of freedom, and it is intended for graduate students and researchers in physics, applied mathematics and mechanics, and mechanical, aerospace, and structural engineering. It may also be suitable for advanced undergraduates in these fields. An intermediate knowledge level of mechanics is required. Many examples and problems including ones from engineering are given.
The author refers to so-called Lagrangean and Hamiltonian mechanics as “analytical mechanics” in principle, and discusses analytical mechanics of constrained systems in this meaning. The book is very different from some recent celebrated textbooks on mechanics such as Foundations of Mechanics, 2nd Edition (Addison-Wesley, Redwood City, CA, 1978), by R Abraham and J E Marsden, and Mathematical Methods of Classical Mechanics, 2nd Edition (Springer-Verlag, New York, 1989), by V I Arnold, which were written from a geometrical point of view (note that mechanics has a long history!). This reviewer feels that this book is difficult to read due to the specialty of symbols and notations and style of descriptions, as well as its length.
The book begins with an explaination of the term analytical mechanics in the Introduction. Several pages are used for expositions of symbols and notations there. In Chapter 1, basic concepts and results of elementary theoretical mechanics are summarized in handbook fashion after prerequisites on vector and tensor algebra are given. In Chapters 2 and 3, kinematics and kinetics of constrained systems are described in the Lagrangean formalism. These are the key chapters of the entire book and use about 500 pages. Some fundamental concepts on constraints like nonholonomicity are introduced, and important techniques like Lagrange’s principle and virtual work are presented. In Chapter 4, impulsive or discontinuous motions are considered and their Lagrangean principles and equations are given. Rigid body dynamics is also discussed in some detail through the first four chapters.
In Chapter 5, the results of Chapters 2 and 3 are extended to systems with nonlinear nonholonomic constraints. In Chapter 6, differential variational principles of constrained systems are treated from simple and unified viewpoints, and the associated kinematico-inertial identities and corresponding generalized equations of motion are given. In Chapter 7, time-integral theorems and the integral variational principle are derived. Finally, in Chapter 8 another formalism of analytical mechanics, ie, Hamiltonian mechanics, is introduced and described in some detail. A long reference list is also given for background, and concurrent and further reading.
Analytical Mechanics will be useful for students and researchers in the related fields who are interested in mechanics of constrained systems, but this reviewer feels that it would be much more useful if it were written in a different format, ie, in a compact style and with the use of standard notations.