PhysicsLibrary CV17 computational resource

Brachistochrone Cycloid and Travel Time

A bead released from rest follows a cycloid under gravity. Compare its descent with a straight path to the same endpoint.

Reference endpoint

All reference cases use a vertical drop of Y = 1 m.

1

Cycloid and straight-line comparison

Depth increases downward.

time-s
x-m
depth y-m
speed-m/s

2

Travel-time comparison

cycloid-s
straight-s
saving-%

3

Numerical travel-time convergence

segments-
estimate-s
relative error-%

4

Endpoint-root solve

iteration-
midpoint theta-rad
bracket width-rad
|residual|-

Reference cases

Three reference brachistochrone paths: endpoints before, at, and after the bottom of the cycloidal arch.

The after-bottom case is the CV17 numerical example, X = 4 m and Y = 1 m.

Saved data and source

Download Julia projectProvenanceLicenseEndpoint-ratio sweep CSVTravel-time convergence CSVBisection history CSV

Generated with Julia @@JULIA_VERSION@@.

Before bottom

Cycloid ending before the bottom
Download CSV

At bottom

Cycloid ending at the bottom
Download CSV

After bottom

Cycloid dipping below the endpoint before rising
Download CSV