Drag either bob to release • drag empty space to pan • wheel or pinch to zoom

3D Double Pendulum Lab

Explore coupling, energy transfer, and chaos.

Gravity+Coupling→Energy exchange→Complex motion

Initial conditions Predictable

Upper release angle65°

Lower release angle25°

Upper length1.00 m

Lower length1.00 m

Upper mass1.00 kg

Lower mass1.00 kg

Gravity9.81 m/s²

Air resistance0.015

Simulation speed1×

Live measurements

Upper angle65.0°

Lower angle25.0°

Upper angular speed0.00 rad/s

Lower angular speed0.00 rad/s

Total energy—

Nearby-path separation0.001°

Orange is height energy; cyan is motion energy. A tiny purple shadow pendulum reveals sensitivity to initial conditions.

Angles & divergence

Upper angleLower angleWhole-system history

Camera & object focus

Zoom100%

No object trackedFree camera

TipTap a pivot or bob

Zoom1.00×

Learning outcomes

Explain how the two arms exchange energy.
Distinguish complex motion from random motion.
Observe sensitivity to tiny changes in initial angle.
Connect mass, length, gravity, and damping to motion.
Use phase and energy data to compare regimes.

Core idea: the system follows deterministic physical laws, yet nearby starting states can separate rapidly. That sensitivity is a hallmark of chaos.

Suggested experiments

Run Gentle coupling, then Chaotic release. Compare divergence.
Change only the lower mass and watch energy transfer.
Turn damping off and observe total mechanical energy.
Use Step to inspect a full rotation frame by frame.

Questions for exploration

Can you predict exactly when the lower bob will flip?
Why can two nearly identical paths look unrelated later?
Which arm carries most kinetic energy at different moments?