Modelling the Golf Downswing as a Driven Double Pendulum: A Lagrangian Analysis of Wrist Release Timing and Clubhead Speed
Richie Liu
09/09/2026
The distance of a golf drive is determined primarily by the speed of the clubhead at the moment of impact. In this paper, the downswing of a driver shot is modelled as a driven double pendulum, consisting of a rigid arm link rotating about a fixed hub and a rigid club link connected at the wrists. The links move in a single plane under a constant hub torque. The equations of motion of the system are derived using Lagrangian mechanics and solved numerically using the fourth-order Runge–Kutta (RK4) method, as no closed-form solution exists. The model is used to investigate how the timing of the wrist release affects the clubhead speed at impact. For a baseline swing with a hub torque of 100 N m and an initial wrist-cock angle of 90°, the model predicts a natural release after the arm has swung through 46.1° and a clubhead speed at impact of 45.0 m s−1 (100.7 mph), consistent with measured amateur and professional driver speeds. Delaying the release until the arm has swung through 118° increases the clubhead speed by 4.4%, while increasing the initial wrist-cock angle and the hub torque produce further, sub-proportional gains. A sensitivity analysis shows that the delayed-release gain remains between 3.0% and 6.0% when each model parameter is varied by a generous margin. These results agree closely with published double pendulum studies of the golf swing and provide a