The task is: "Build a single-page web app and write it ALL into one self-contained file named index.html in the current directory: CSS in a <style> tag, JS in a <script> tag, inline — do not create se...First, I need to recall the correct equations of motion for a double pendulum.

For a double pendulum with masses m1, m2, lengths l1, l2, gravity g.

The angles θ1, θ2 from vertical.

The accelerations:

Let me derive or recall:

a1 = (g*(2 m1 + m2) * sin(θ1) + m2 * g * sin(θ1 - 2*θ2) + 2 * sin(θ1 - θ2) * m2 * (l2 * ω2**2 + l1 * ω1**2 * cos(θ1 - θ 2))) / (l1 * (2*m1 + m2 - m2 * cos(2*(θ1 - θ2))))

No, signs: since θ from vertical, sin terms are negative for torque.

The directory is empty. I need to create index.html with a self-contained single-page web app simulating a chaotic double pendulum.
First, I need to recall the correct equations for a double pendulum.

The standard equations for a double pendulum with masses m1, m2, lengths l1, l2, angles θ1, θ2 from the downward vertical, gravity g.

The accelerations:

Let’s define:

c1 = cos(θ1)

 c2 = cos(θ1 - θ2)

  s1 = sin(θ1)

  s2 = sin(θ1 - θ2)

  s3 = sin(θ2)

Then, the angular accelerations α1, α2.

A common form is:

denom = l1*l1*(m1+m 2) + l2*l2*m2 + 2*m2*l1*l2*cos(θ1-θ2)

Then:

a1 = [ -g*(2*m1 + m2)*s1 - m2*g*s2*cos(θ1-θ2) - m2*l2*ω2 ²*s2*sin(θ1-θ2) - m1*l1*ω1²*s1 - 2*m2*l1*ω1²*s2*cos(θ1-θ2) ] / denom wait, better to use the standard one I recalled earlier.

The file has been created successfully. Let me verify it exists and check its size.

The single file is done and present.