The double pendulum is a classic example of a nonlinear dynamical system exhibiting deterministic chaos. To model its motion, we use Lagrangian Mechanics, focusing on energy states rather than force vectors.1. Generalized CoordinatesThe system is defined by two angles, θ₁ and θ₂, measured from the vertical. The positions of the masses (m₁, m₂) are:• Mass 1: x₁ = L₁ sin(θ₁), y₁ = -L₁ cos(θ₁)• Mass 2: x₂ = x₁ L₂ sin(θ₂), y₂ = y₁ - L₂ cos(θ₂)2. Kinetic (T) & Potential (V) Energy• T = ½m₁v₁² ½m₂v₂²•
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