PM014
186 pages
ISBN 2-921120-20-8
1992 |
Florin N. Diacu
The text is based on a series of lectures given at the CRM in 1991. It contains many recent results as well as old ones regarded from a modern point of view. The main purpose is the study of the singularities arising in the equations of motion and in the solutions of the classical N-body problem of celestial mechanics, using
tools of dynamical systems theory. Topics include criteria for existence of solutions
with singularities like the theorems of von Zeipel, Pollard and Saari, examples
of solutions leading to pseudocollisions, an introduction to the growing theory
of central configurations, regularization techniques for collisions, McGehee transformations
and the idea of the collision manifold, structural stability of homothetic
orbits, simultaneously binary collisions and series solutions attempts for the N-body
problem. The text offers a modern introduction to celestial mechanics from a
mathematical point of view.
Contents
- The N-body problem
- The nature of singularities
- The theorem of von Zeipel
- The criteria of Pollard and Saari
- Solutions free of pseudocollisions
- Examples of pseudocollisions
- Central configurations
- Regularization of collisions
- Triple collision in the rectilinear three-body problem
- The collision manifold
- Structural stability of homothetic orbits
- Simultaneous binary collisions
- Time regularization of partial collisions
- The solution of the N-body problem
To order: crmbooks@CRM.UMontreal.CA.
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