Global Formulations of Lagrangian and Hamiltonian
Dynamics on Manifolds
Back Cover Copy
This book provides an accessible introduction to the variational
formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis
on global descriptions of the dynamics, which is a significant conceptual
departure from more traditional approaches based on the use of local
coordinates on the configuration manifold. In particular, we introduce a
general methodology for obtaining globally valid equations of motion on
configuration manifolds that are Lie groups, homogeneous spaces, and
embedded manifolds, thereby avoiding the difficulties associated with
coordinate singularities.
The material is presented in an approachable fashion by considering
concrete configuration manifolds of increasing complexity, which then
motivates and naturally leads to the more general formulation that
follows. Understanding of the material is enhanced by numerous in-depth
examples throughout the book, culminating in non-trivial applications
involving multi-body systems.
This book is written for a general audience of mathematicians,
engineers,
and physicists with a basic knowledge of mechanics. Some basic background
in differential geometry is helpful, but not essential, as the relevant
concepts are introduced in the book, thereby making the material
accessible to a broad audience, and suitable for either self-study or as
the basis for a graduate course in applied mathematics, engineering, or
physics.
Taeyoung Lee,
Associate Professor of Mechanical and Aerospace Engineering, George
Washington University. Melvin Leok,
Professor of Mathematics, University of
California, San Diego. N.
Harris McClamroch, Professor Emeritus of Aerospace
Engineering, University of Michigan, Ann Arbor.
