See the explanation for this in here: [ Ссылка ]

The Brachistochrone curve deals with a bead sliding frictionlessly under the influence of a uniform gravitational field.
In case of rolling frictionlessly, it loses all its significance to be the fastest and needs calculations to decide the fastest curve in each individual experiment (it still can end up being the fastest).
This simulation, as well as the Vsauce experiment (linked above), does not show the real Brachistochrone curve experiment, but as can be seen in both cases (as well as in many others), still, the Brachistochrone curve provides a short time to reach the end point.
In summary, this means the Vsauce video is wrong. One has to build a path (preferably out of a low friction material such as sheet metal) and fully lubricate its surface with oil and then slide an equally lubricated object on top of the different curves to determine the fastest one. Such experiment, will transfer better the idea behind The Brachistochrone curve experiment, in contrast to the ones where objects just roll over it.

свернуть