Watch chaos unfold while a measured energy invariant keeps the numerics honest.
See it run - a worked example, 100% in this browser tab
The problem
Chaotic simulations are easy to get visually plausible but wrong, and most demos give no honest signal of whether the numerics are actually faithful.
The local-first solution
This plugin integrates the exact double-pendulum Lagrangian with RK4 in the browser and certifies the run by measuring the relative drift of the conserved total energy, mapping that real residual to the GeoNum trust ladder.
What it does
Exact two-link planar Lagrangian reduced to a 4D first-order system
Classical 4th-order Runge-Kutta integration with selectable step size
Measured max relative energy drift normalized by the gravitational energy scale
Trust verdict mapped from that real residual (EXACT through UNRELIABLE)
Seeded PRNG jitter to expose sensitive dependence on initial conditions
Honest scope
Exact equations of motion; the RK4 truncation drift is a genuine residual that shrinks like dt^4. A green verdict certifies the energy invariant is conserved to tolerance - it does NOT certify long-term trajectory, which is intrinsically unpredictable past the Lyapunov horizon. This is a demonstrator, not engineering advice.
Authorities cited
Goldstein, Poole, Safko (2002). Classical Mechanics, 3rd ed., Ch. 1-6 - the double-pendulum Lagrangian and equations of motion.
Strogatz (2015). Nonlinear Dynamics and Chaos, 2nd ed. - sensitive dependence on initial conditions and the Lyapunov horizon.
Integrate a chaotic trajectory
Run the pendulum in the browser and save the energy-certified result to Sandbox, attach it to a Worklog case, or route it into a Gate client portal. Nothing leaves your machine.