  The Arnold Sommerfeld effect is an intriguing resonance capture and release
series of events originally demonstrated in 1902. A single event is studied
using a two degree of freedom mathematical model of a motor with imbalance
mounted to laterally restricted spring connected cart. For a certain power
supplied, in general the motor rotates at a speed consistent with a motor on a
rigid base. However at speeds close to the natural frequency of the cart, it
seemingly takes on extra oscillations where for a single rotation it both
speeds up and then slows down. Therefore in a standard experimental
demonstration of the effect, as the supplied torque force is increased or
decreased, this may give the illusion that the stable operation of the motor is
losing and gaining stability. This is not strictly the case, instead small
oscillations always present in the system solution are amplified near the
resonant frequency. The imbalance in the motor causes a single resonance curve
to fold back on itself forming two fold bifurcations which leads to hysteresis
and an asymmetry between increasing and decreasing the motor speed. Although as
outlined the basic mechanism is due the interplay between two stable and one
unstable limit cycles, a more complicated bifurcation scenario is observed for
higher imbalances in the motor. The presence of a Z2 phase space symmetry
tempers the dynamics and bifurcation picture.
