École Nationale Supérieure de
Techniques Avancées

Abstract

The Newtonian N-body problem has been a reference problem in classical physics. It describes the motion of N bodies gravitationally attracted to each other. With the beginning of mathematical computation and the possibility to run simulations, it is known that for N 3, the system chaotic. Few analytical solutions emerged from this problem but other solutions have been observed and highlighted the dependence to the initial conditions. Using and comparing different numerical tools, the same phenomenon is seen for N bodies (electrons) attacted to a central body (nucleus) but repelling each other. In a plane or in a 3D-space, there are sets of initial values for which the interaction between the electrons is such that the motion is chaotic. Moreover, for some specific initial values, it is possible to get periodic solutions.