PM014
186 pages
ISBN 2921120208
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 Nbody 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 Nbody
problem. The text offers a modern introduction to celestial mechanics from a
mathematical point of view.
Contents
 The Nbody 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 threebody problem
 The collision manifold
 Structural stability of homothetic orbits
 Simultaneous binary collisions
 Time regularization of partial collisions
 The solution of the Nbody problem
To order: crmbooks@CRM.UMontreal.CA.
