Brachistochrone curve

A brachistochrone curve (from Ancient Greek βράχιστος χρόνος  (brákhistos khrónos) 'shortest time'),^[ or  curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides  frictionlessly under the influence of a uniform gravitational field to a given end point in the shortest time. The problem was posed by  Johann Bernoulli in 1696.

Here, it is simulated in Abaqus/Explicit.