University of Minnesota
School of Physics & Astronomy

Physics and Astronomy Calendar

Monday, December 3rd 2018
12:30 pm:
FTPI Seminar in Tate 301-20
Speaker: Alexander Turbiner
Subject: Choreography in (non)-Newtonian gravity

By definition the choreography (dancing curve) is the trajectory
on which n classical bodies move chasing each other without collisions.
The first choreography (the remarkable Figure Eight) at zero angular
momentum was discovered unexpectedly by C Moore (Santa Fe) at 1993
for 3 equal mass bodies in R^3 Newtonian gravity numerically.
At the moment about 6,000 choreographies are known, all numerically
in Newtonian gravity. A number of 3-body choreographies is known
for Lenard-Jones potential again numerically.

Do exist (non)-Newtonian gravity for which dancing curve is known
analytically? - Yes, one example is known - it is algebraic lemniscate by
Jacob Bernoulli (1694) - and it will be the subject of the talk.
Astonishingly, Newtonian Figure Eight coincides with algebraic lemniscate
with accuracy 10 - 7 .

Faculty Host: Mikhail Shifman

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