Stability analysis of the Gyroscopic Power Take-Off wave energy point absorber

• Nonlinear equations of motions of a gyroscopic PTO wave energy point absorber have been derived.
• Simplified decoupled equations of motion of the float are indicated for monochromatic linear waves.
• The equations of motion of the ring become nonlinear with parametric excitation.
• The absorbed electric power at synchronisation is different in the two directions.
• The stability at synchronisation depends on the level of the absorbed power.

The Gyroscopic Power Take-Off (GyroPTO) wave energy point absorber consists of a float rigidly connected to a lever. The operational principle is somewhat similar to that of the so-called gyroscopic hand wrist exercisers, where the rotation of the float is brought forward by the rotational particle motion of the waves. At first, the equations of motion of the system are derived based on analytical rigid body dynamics. Next, assuming monochromatic waves simplified equations are derived, valid under synchronisation of the ring of the gyro to the angular frequency of the excitation. Especially, it is demonstrated that the dynamics of the ring can be described as an autonomous nonlinear single-degree-of-freedom system, affected by three different types of point attractors. One where the ring vibrations are attracted to a static equilibrium point indicating unstable synchronisation and two types of attractors where the ring is synchronised to the wave angular frequency, either rotating in one or the opposite direction. Finally, the stability conditions and the basins of attraction to the point attractors defining the synchronised motion are determined.