Celestial Choreographies

Lezing
vri 20 nov 2009, 14:30
Sterre S9, V2

Wie-doet-wat-colloquium met André Vanderbauwhede als spreker. De lezing vereist geen specifieke voorkennis van het vakgebied.

Newton's gravitation law leads for two bodies to the Kepler laws which describe all possible orbits by simple formulas. This situation changes dramatically when three or more bodies are involved; except for a few very special motions it is no longer possible to write down solutions in closed form, and chaos (whatever way one wants to define this) comes into the picture. But however complicated the system may be, it was already observed by Poincaré that the periodic orbits form a kind of "backbone" through which one can penetrate and understand the full system. In this talk we describe a few variants of a continuation approach which allows to calculate (numerically) a large collection of such periodic orbits. For our main example (with three or four bodies) the starting point will be so-called choreographies, a new class of special solutions which have been discovered during the last decade. If time permits we will also illustrate the method with results on the periodic solutions of the restricted three body problem. The talk will be non-technical, and abundantly illustrated with graphics and movies.