Physical Principles & Mathematical Derivation
Derived via Euler-Lagrange mechanics, the double pendulum is a textbook Hamiltonian system exhibiting deterministic chaos at high energies: although governed by exact deterministic equations with strictly conserved total energy (KE + PE = const), microscopic changes in starting angle diverge exponentially over seconds!
Questions & Concepts
What physical equation governs Chaotic Double Pendulum Simulator (Exact Lagrangian RK4)?
L = T − V, d/dt(∂L/∂θ̇ᵢ) − ∂L/∂θᵢ = 0 — Derived via Euler-Lagrange mechanics, the double pendulum is a textbook Hamiltonian system exhibiting deterministic chaos at high energies: although governed by exact deterministic equations with strictly conserved total energy (KE + PE = const), microscopic changes in starting angle diverge exponentially over seconds!
How are the equations of motion integrated in this simulation?
Nonlinear differential equations are integrated at 240–300 Hz substeps using classical 4th-order Runge-Kutta (RK4) to maintain strict Hamiltonian energy accuracy.