Preface; 1. The central force problem; 2. Conic sections; 3. The Kepler problem; 4. The dynamics of the Kepler problem; 5. The two-body problem; 6. The n-body problem; 7. The three-body problem; 8. The differential geometry of the Kepler problem; 9. Hamiltonian mechanics; 10. The topology of the Kepler problem; Bibliography; Index.
Hansjorg Geiges is Professor of Mathematics at the University of Cologne. He has received several teaching awards, and an EMS prize for mathematical exposition. His book An Introduction to Contact Topology (Cambridge, 2008), has become a highly cited standard reference for the field.
'The Geometry of Celestial Mechanics offers a fresh look at one of the most celebrated topics of mathematics ... I would gladly recommend this book ...' Anil Venkatesh, Mathematical Association of America Reviews 'Because much of the geometric theory, the many historical notes, and the exercises in the book are not found in other contemporary books on celestial mechanics, the book makes a great addition to the library of anyone with an interest in celestial mechanics.' Lennard Bakker, Zentralblatt MATH 'The book fulfills the authors quest, as stated in the preface, 'for students to experience differential geometry and topology 'in action' (in the historical context of celestial mechanics) rather than as abstractions in traditional courses on the two subjects.' Lennard F. Bakker, Mathematical Reviews