  When it opened to pedestrian traffic in the year 2000, London's Millennium
Bridge exhibited an unwanted, large, side-to-side oscillation which was
apparently due to a resonance between the stepping frequency of walkers and one
of the bridge modes. Models for this event, and similar events on other
bridges, have been proposed. The model most directly addressing the
synchronization mechanism of individual walkers and the resulting global
response of the bridge-pedestrian system is one developed by Eckhardt et al.
This model treats individual walkers with a phase oscillator description and is
inherently high dimensional with system dimensionality (N+2), where N is the
number of walkers. In the present work we use a method proposed by Ott and
Antonsen to reduce the model of Eckhardt et al. to a low dimensional dynamical
system, and we employ this reduced description to study the global dynamics of
the bridge/pedestrian interaction. More generally, this treatment serves as an
interesting example of the possibility of low dimensional macroscopic behavior
in large systems of coupled oscillators.
