BRACHISTOCHRONE RACE LAB
THREE.JS r160 READY
3D view unavailable. The timing model below remains usable.
TIME IS NOT DISTANCE
The shortest route can lose.
Release both beads from rest. One follows the shortest chord; the other follows the endpoint-matched cycloid under the same gravity.
Choose a winner, then release both beads.
The model is ready for the 10 m by 5 m endpoint.
Solve x=a(theta-sin theta), y=a(1-cos theta).
Counterexample: at constant speed, shorter distance means shorter time, so the straight route wins.
TRANSFER: move the endpoint. The curve changes with it; it is not just any curved rail. This model assumes uniform gravity, frictionless point masses, no drag, and no rolling inertia.