Pendulum models of ponytail motion during walking and running


Journal Article

Steady-state motions of a woman's 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 woman's 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. © 2013 Elsevier Ltd.

Full Text

Duke Authors

Cited Authors

  • Plaut, RH; Virgin, LN

Published Date

  • August 5, 2013

Published In

Volume / Issue

  • 332 / 16

Start / End Page

  • 3768 - 3780

Electronic International Standard Serial Number (EISSN)

  • 1095-8568

International Standard Serial Number (ISSN)

  • 0022-460X

Digital Object Identifier (DOI)

  • 10.1016/j.jsv.2013.02.016

Citation Source

  • Scopus