Geometric Chaos Demo for a Double Pendulum

This example demonstrates the hallmark chaotic behavior of a double pendulum by animating how its bob positions evolve over time: tiny differences in initial conditions lead to rapidly diverging motion. The key mathematics includes nonlinear dynamics governed by (second-order) differential equations, the numerical time-stepping idea (via a chosen time step), and geometric constructions that encode motion using vectors and orthogonal (tangent/normal) directions. Construction highlights extracted from the command list: Circle, Arc, Point, Segment, UnitOrthogonalVector, and PolyLine are used to build the circular arcs and key points, then connect them with segments; objects such as l and O define the pivot and baseline geometry; parameters and intermediate quantities for the first arm/bob are represented by c1, arc1, P1, M1, r1 together with related tangent/normal components (e.g., vt1, gt1, n1, gt1); analogous elements for the second arm/bob are given by c2, arc2, P2, M2, r2 and vt2/gt2/n2; anima and the time variables t, dt, t0, t1, tt, tPausa coordinate the animation. This is well-suited for high school to undergraduate instruction on modeling, numerical simulation, dynamical systems, and interactive exploration of chaos in GeoGebra.