This third edition text provides expanded material on the restricted
three body problem and celestial mechanics. With each chapter containing
new content, readers are provided with new material on reduction,
orbifolds, and the regularization of the Kepler problem, all of which
are provided with applications.
The previous editions grew out of graduate level courses in mathematics,
engineering, and physics given at several different universities. The
courses took students who had some background in differential equations
and lead them through a systematic grounding in the theory of
Hamiltonian mechanics from a dynamical systems point of view.
This text provides a mathematical structure of celestial mechanics ideal
for beginners, and will be useful to graduate students and researchers
alike.
Reviews of the second edition:
"The primary subject here is the basic theory of Hamiltonian
differential equations studied from the perspective of differential
dynamical systems. The N-body problem is used as the primary example of
a Hamiltonian system, a touchstone for the theory as the authors develop
it. This book is intended to support a first course at the graduate
level for mathematics and engineering students. ... It is a
well-organized and accessible introduction to the subject ... . This is
an attractive book ... ." (William J. Satzer, The Mathematical
Association of America, March, 2009)
"The second edition of this text infuses new mathematical substance and
relevance into an already modern classic ... and is sure to excite
future generations of readers. ... This outstanding book can be used not
only as an introductory course at the graduate level in mathematics, but
also as course material for engineering graduate students. ... it is an
elegant and invaluable reference for mathematicians and scientists with
an interest in classical and celestial mechanics, astrodynamics,
physics, biology, and related fields." (Marian Gidea, Mathematical
Reviews, Issue 2010 d)
