Pendulum models of ponytail motion during walking and running

Steady-state motions of a womanʹs ponytail during level, straight, walking and running are examined. Based on reported data, formulas have been developed for the relationship of the forward speed to the frequencies of vertical and sideways motion of the head, and of the form of that motion. The ponytail is modeled as a compound pendulum or a multi-bar pendulum with 2, 3, or 5 rigid bars. Motions in the vertical plane perpendicular to the direction of progression are analyzed. Rotational springs and dashpots are placed at the joints, and aerodynamic damping (air drag) is included. Attention is focused on the variation of the amplitudes of the bars as the womanʹs walking speed and then running speed increase. An example of three-dimensional motions of a spherical-pendulum model also is included. Experiments were conducted on a double pendulum with parabolic applied motion at the top. The damping is modeled by rotational friction (i.e., a constant resisting moment at the top and internal joints), and the numerical results agree well with the test data.