Kalender Department Mathematik

Thu, 13.12.2018, 16:15

Thu, 13.12.2018, 18:00
Symplectic reduction of the 3-body problem in 4-dimensional space
AG Mathematische Physik

Referent: Holger Dullin (Sydney)
Veranstalter: AG Mathematische Physik
Raum: U1

The N-body problem in d-dimensional space has symmetry group SE(d).
Centre of mass reduction leads to a system with SO(d) symmetry acting
diagonally on positions and momenta. For N=3, d=4 reduction of the SO(4)
symmetry is unusual because the tensor of inertia is non-invertible.
The fully reduced system has 4 degrees of freedom and a Hamiltonian that 
is not polynomial in the momenta. Some properties of this Hamiltonian 
will be discussed, in particular we show that there are relative equilibria
that are minima of this Hamiltonian.
Joint work with Juergen Scheurle