Lagrangian Double Pendulum – AP Physics C

Learning Objectives

Observe chaotic behavior from deterministic equations

Understand Lagrangian formulation: L = T − V

Recognize sensitivity to initial conditions

Track energy conservation in numerical simulation

Key Concepts

L = T − V (Lagrangian)
Euler-Lagrange: d/dt(∂L/∂θ̇) − ∂L/∂θ = 0
Chaotic: tiny Δθ₀ → wildly different trajectories
RK4 numerical integration