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Theory of Orbits treats celestial mechanics as well as stellar dynamics from the common point of view of orbit theory, making use of concepts and techniques from modern geometric mechanics. It starts with elementary Newtonian mechanics and ends with the dynamics of chaotic motion. The two volumes are meant for students in astronomy and physics alike. Prerequisite is a physicist's knowledge of calculus and differential geometry.
Half a century ago, S. Chandrasekhar wrote these words in the
preface to his 1 celebrated and successful book: In this monograph
an attempt has been made to present the theory of stellar dy namics
as a branch of classical dynamics - a discipline in the same
general category as celestial mechanics. [ ... ] Indeed, several of
the problems of modern stellar dy namical theory are so severely
classical that it is difficult to believe that they are not already
discussed, for example, in Jacobi's Vorlesungen. Since then,
stellar dynamics has developed in several directions and at var
ious levels, basically three viewpoints remaining from which to
look at the problems encountered in the interpretation of the
phenomenology. Roughly speaking, we can say that a stellar system
(cluster, galaxy, etc.) can be con sidered from the point of view
of celestial mechanics (the N-body problem with N" 1), fluid
mechanics (the system is represented by a material con tinuum), or
statistical mechanics (one defines a distribution function for the
positions and the states of motion of the components of the
system).
Half a century ago, S. Chandrasekhar wrote these words in the
preface to his l celebrated and successful book: In this monograph
an attempt has been made to present the theory of stellar dy namics
as a branch of classical dynamics - a discipline in the same
general category as celestial mechanics. [ ... J Indeed, several of
the problems of modern stellar dy namical theory are so severely
classical that it is difficult to believe that they are not already
discussed, for example, in Jacobi's Vorlesungen. Since then,
stellar dynamics has developed in several directions and at var
ious levels, basically three viewpoints remaining from which to
look at the problems encountered in the interpretation of the
phenomenology. Roughly speaking, we can say that a stellar system
(cluster, galaxy, etc.) can be con sidered from the point of view
of celestial mechanics (the N-body problem with N " 1), fluid
mechanics (the system is represented by a material con tinuum), or
statistical mechanics (one defines a distribution function for the
positions and the states of motion of the components of the
system).
This textbook treats Celestial Mechanics as well as Stellar Dynamics from the common point of view of orbit theory making use of the concepts and techniques from modern geometric mechanics. It starts with elementary Newtonian Mechanics and ends with the dynamics of chaotic motions. The book is meant for students in astronomy and physics alike. Prerequisite is a physicist's knowledge of calculus and differential geometry. Volume 1 begins with classical mechanics and a thorough treatment of the 2-body problem, including regularization, followed by an introduction to the N-body problem with particular attention given to the virial theorem. Then the authors discuss all important non-perturbative aspects of the 3-body problem. A final chapter deals with integrability of Hamilton-Jacobi systems.
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