Analytical mechanics. A comprehensive treatise on the dynamics of constrained systems for engineers, physicists and mathematicians (Q2782589)

This is a monumental treatise on the analytical mechanics (AM), which, according to this reviewer's opinion, is going to become a reference book on the subject. Even for well-developed fields of science, and analytical mechanics is definitely such a field, books of approximately 1400 pages are seldom written. The books like this one are not read at one sitting, and understanding of its content, ideas that it brings, and its importance, requires time. It seems, however, that this treatise on AM is in line with well-known great books on the subject starting from Whittaker (1904). It should not be missed by anybody working in the area of analytical dynamics or only wanting to understand major problems of the subject. NEWLINENEWLINENEWLINEThe book treats, from engineering point of view, all important parts of AM that are subject of present interest and research. In chapter 1 the basic concepts and equations of particle and rigid body mechanics are presented: elements of vector and tensor calculus, geometry of motion, Eulerian angles, quasi-coordinates, inertial and noninertial frames of reference, laws of motion etc. Chapter 2 presents kinematics of constrained motion with detailed discussion on different forms of resulting kinematical relations: noncommutativity, nonholonomicity, Pfaffian form etc. The Frobenius theorem for testing the nonholonomicity is also included. Chapter 3 deals with equations of motions of constrained system. The virtual displacement method is presented clearly and in the line with (classical) Hamel approach. This chapter contains excellent discussion on the method of virtual work with many examples, including an example of servo or control constraints. It is also stated in this chapter that central assumption in the Lagrange's principle (the virtual work of ideal reaction forces is equal to zero) may be viewed as a constitutive postulate for ideal constraints. To this reviewer, the presentation at the end of the appendix of chapter 3 is, probably, not relevant for understanding the core problem that was already very well elaborated. NEWLINENEWLINENEWLINEChapter 4 treats in detail impulsive motion. Important theorems of Carnot, Kelvin, Bertrand and Robin are presented. Both generalized and quasi-coordinates are treated. Noticeably, the newer theories of impact (that are more mathematical, like distributional model of impact) are not presented. In chapter 5 the author discusses nonlinear nonholonomic constraints, a subject of great importance and interest in actual research. This chapter contains generalizations of Pfaffian equations, Hamel equations, and Chaplygin-Voronets equations. In chapter 6 differential variational principles of Lagrange, Gauss, Hertz and Mangeron-Deleanu are presented from a unified viewpoint. The associated kinematic-inertial identities are then introduced to obtain the generalized equations of motion (Nielsen, Tsenov, Dolaptschiew). Chapter 7 presents time-integral theorems with linear and nonlinear nonholinomic constraints, as well as variational principles of Lagrange, Hamilton, Jacobi, Holder, Voss, Suslov, Voronets and Hamel. This chapter ends with nicely elaborated difference between Hamilton's variational principle for nonholonomic systems and constrained variational principles of variational calculus. Chapter 8 presents Hamiltonian canonical method of AM. It treats Hamilton-Jacobi theory, canonical transformations, Noether's theorem, adiabatic invariants and canonical perturbations. The derivation of canonical equations, in line with the general philosophy of the book, is based on central Lagrangian equation (not on Legendre's transformation). The book ends up with index and extensive reference list. NEWLINENEWLINENEWLINEIn conclusion, we may say that this book treats allmost all important questions of (engineering) AM. It contains references to recent contrubitions as well as references to contribution of older authors. Often, the author gives critical remarks on some contemporary contributions in AM, together with historical remarks. The main characteristic of the author's approach is a consequent use of virtual displacement method. The book presents an important up-to-date account of AM, and is a wellcome addition to the present literature on the subject. The book will be of interest to all researchers in AM, as well as to graduate students in engineering, physics and mathematics.