The present article describes an experimental study of the dynamics
of a small magnetic particle moving on the flat horizontal free surface of a
rotating liquid and submitted to a magnetic field that decreases with distance
from a dipole magnet. The particle is kept at the surface by interface forces
and its motion is bidimensional. For a constant external force, its behaviour
displays a transition at a threshold angular rotation velocity Ω = Ωc.
Below the threshold, the particle remains at a fixed point; above the
threshold, its trajectory tends towards a limit cycle of ovoidal shape and
size increasing with Ω.
A phenomenological modification of the equation that describes the motion of
the particle is suggested in order to represent the influence of capillary
effects on the particle trajectory: an effective drag coefficient is
introduced that decreases the inertial response time of the particle.
The numerical integration of the equation agrees with experimental
observations. Nonlinear effects for a time-dependent magnetic field have
been studied in the case of a square wave variation of frequency ω.
The shape of the Poincaré sections is shown to depend on the ratio ω/Ω.
Starting from the disc angular coordinate, a circle map may be constructed
which shows an almost one-dimensional behaviour.