How long do two double pendulums started 0.1° apart swing together?
The Reference (cyan pivot) and Perturbed (orange pivot) pendulums move in step for the first few swings; after about 210 ticks, 7 simulated seconds, their lower bobs are in visibly different places.
Try thisChoose Gentle swings (upper-angle 15, lower-angle 10, the same 0.1° difference). separation stays below about 0.013 for a full simulated minute: at small angles the motion is close to two coupled linear oscillators, and the gap does not grow.
About this model
A double pendulum, one pendulum hanging from another, is a standard example of deterministic chaos: at large swings, two starts that differ by a fraction of a degree end up in unrelated motion within a few swings. This model runs two side by side, one started 0.1° from the other, and plots the distance between their lower bobs.
Each pendulum is a fixed pivot and two point-mass bobs (the lower bob's mass is lower-mass, default 1) joined by massless rigid rods. Nothing in the model knows it is a pendulum: each tick applies gravity (9.81 × mass) to every bob and advances the mechanics library by 1/30 s, in substeps of at most 1/240 s, with SHAKE/RATTLE corrections that hold each rod at its starting length. There is no friction, and energy is conserved only approximately.
All seven controls apply at setup, so press Reset after changing them. Identical twins sets difference to 0: the two then agree to within 0.001 for about 35 simulated seconds, until floating-point roundoff (they hang at different x positions) grows like any other small difference.
IdeaDouble pendulum mechanics · org
MathPetsMathPets · org
