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Home » Hamiltonian Colloquium: Symplectic reduction of the 3-body problem in 4-dimensional space

Seminar

Hamiltonian Colloquium: Symplectic reduction of the 3-body problem in 4-dimensional space October 22, 2018 (04:00 PM PDT - 05:00 PM PDT)
Parent Program:
Location: MSRI: Simons Auditorium
Speaker(s) Holger Dullin (University of Sydney)
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Abstract/Media

The N-body problem in d-dimension 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 complicated because the tensor of inertia is non-invertible.

The fully reduced system has 4 degrees of freedom and a Hamiltonian thatĀ 

is not polynomial in the momenta. The most surprising property of theĀ 

reduced Hamiltonian is that it has equilibria that are minima.

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