Dinosaur Trackway Speed: Pendulum-Swing Model

This is the 2D companion to the dinosaur trackway speed reconstructor. Where the 3D version applies Alexander's (1976) empirical trackway equation — a curve fitted to living animals — this simulator instead treats the swinging leg between footfalls as a genuine rigid physical pendulum pivoting at the hip and integrates its exact, nonlinear equation of motion. Because that equation has no elementary closed-form solution, the half-swing time is obtained from the complete elliptic integral of the first kind via the arithmetic-geometric-mean algorithm, cross-checked against a direct Runge-Kutta integration of the ODE. The result is a second, fully independent speed estimate from the same fossil measurements, plotted alongside Alexander's empirical value so you can see exactly where first-principles mechanics and empirical curve-fitting agree — and, for brisker running gaits whose aerial phase a free pendulum cannot capture, where they sharply part ways.