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Monday, December 3rd 2018

12:30 pm:

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}
.

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