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PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20191129T104744Z
DTSTART:20191205T150000Z
DTEND:20191205T160000Z
SUMMARY: Philip Arathoon - Singular reduction of the 2-body problem on th
e 3-sphere and the 4-dimensional Lagrange top
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}ao9-k1296q5
k-b5w5et
DESCRIPTION:Title: Singular reduction of the 2-body problem on the 3-sphe
re and the 4-dimensional Lagrange top\n\nAbstract:\n\nFor the motion of
two attracting bodies in Euclidean space\, the translational symmetry re
duces the system to that of the usual Kepler problem. For two bodies on
a sphere this is no longer the case as no such group of translational sy
mmetries existâ€”except for when the sphere in question is the 3-sphere. I
n this case\, both left and right translations act as symmetries\, and t
ogether generate the action of SO(4). Furthermore\, owing to the double
cover of SO(4)\, the dynamics for the 2-body problem on the sphere doubl
e cover the dynamics of a symmetric heavy top in 4 dimensions. The top i
s a generalised Lagrange top possessing an axis of symmetry within the b
ody. The left and right SO(3) reductions\, about the line of gravity and
the line of symmetry in the top\, correspond under the double cover to
the left and right translations of the 2-body problem. We investigate th
e geometry of the reduced manifolds and study their relative equilibria.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams Room 1\, Alan Turing Building\, Manchester
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