In addition the bob reverses its vertical direction half way.Senax wrote: ↑Sun Jan 22, 2023 9:28 pmBut for a shallow pendulum swing from points A and B at the same heightFletcher wrote: ↑Sun Jan 22, 2023 8:53 pm FWIW .. In my experience Agor it helps to build a simple mind picture and context when attempting to analyze an answer to a question of a mechanical nature such as the Brachistochrone.
In this case I extended the context to a bob-weighted pendulum or a rim-weight on a circle wheel acting under gravity. n.b. both pend rod and circle background having zero mass.
In both examples above the radius doesn't change as they swing downwards and then upwards .. and their KE's at any given height loss or regain are identical .. just like the Brachistochrone.
and a deep pendulum swing from points the same points A to B the
time taken is not the same.
The shallow swing takes longer than the deep swing.
It does not reverse its horizontal direction.