
Review: "This wellwritten and expansive book is
ambitious in its scope in that it aims at sound and thorough pedagogy as
far as its subject matter is concerned, and it also aims at preparing the
reader for computational work: note the subtitle, viz., “A geometric
approach to modeling and analysis.” In that sense it is a particularly
timely book, seeing that we have computing power at our disposal like
never before. There are many good examples accompanying or even guiding
the text, as well as extensive problem sets for the properly serious
student. This book hits its targets square and should prove very valuable
to its readership, be they mathematicians, engineers, or physicists."
Michael Berg, MAA
Reviews, November 2017.
Review: "The starting point of this
impressive textbook is the important fact that there are remarkable
situations where the variables that describe a dynamical system do
not lie in a vector space (i.e., a simple flat algebraic structure)
but rather lie in a geometrical setting allowing the differential
calculus, namely a differential manifold. ... In conclusion, this
book is extremely useful for each reader who wishes to develop a
modern knowledge of analytical mechanics."
Mircea
Crâşmăreanu,
zbMATH 1381.70005,
2018.
Review: "This book presents a monograph on
foundational geometric principles of Lagrangian and Hamiltonian dynamics
and their application in studying important physical systems. ... The
emphasis in this book is on global descriptions of Lagrangian and Hamiltonian dynamics, where suitable
mathematical tools are available, via global analysis of dynamical
properties. This treatment is novel and unique and it is the most
important distinction and contribution of this text to the existing
literature. Throughout the book numerous examples of Lagrangian and
Hamiltonian systems are included, which are especially useful to
illustrate the concepts and the way in which the developed theory can be
applied in practical situations. ... The book under review succeeds in all
its objectives and sets the stage for a treatment of computational issues
associated with Lagrangian and Hamiltonian dynamics that evolve on a
configuration manifold. It is very clearly written and it will be
especially useful both for beginning researchers and for graduate students
in applied mathematics, physics, or engineering.
M. Eugenia Rosado María, AMS
Mathematical Reviews, 2018.
Melvin Leok is a professor of mathematics at the University of California, San Diego. His research focuses on computational geometric mechanics, computational geometric control theory, discrete geometry, and structurepreserving numerical schemes, and particularly how these subjects relate to systems with symmetry. He received his Ph.D. in 2004 from the California Institute of Technology in Control and Dynamical Systems under the direction of Jerrold Marsden. He is a Simons Fellow in Mathematics, a threetime NAS Kavli Frontiers of Science Fellow, and has received the NSF Faculty Early Career Development (CAREER) award, the SciCADE New Talent Prize, the SIAM Student Paper Prize, and the Leslie Fox Prize (second prize) in Numerical Analysis. He has given plenary talks at Foundations of Computational Mathematics, NUMDIFF, and the IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control. He serves on the editorial or advisory boards of the Journal of Nonlinear Science, the International Journal of Computer Mathematics, the Journal of Geometric Mechanics, and the Journal of Computational Dynamics, and has served on the editorial boards of the SIAM Journal on Control and Optimization, and the LMS Journal of Computation and Mathematics.
SciCADE New Talent Award  SIAM Student Paper Prize  Leslie Fox Prize 