Dynamical analysis of an anemoscope in the phase plane

We study the dynamical aspects of an anemoscope indicating a wind direction by constructing a model in the discrete view of fluid. Due to the non-linearity of the rotational equation, the geometrical method is applied for the qualitative analysis. For a given wind direction, there are two fixed points of the parallel and anti-parallel configurations. Near the anti-parallel configuration of the stable fixed point, the anemoscope performs a damped harmonic oscillation. It can be noteworthy that there is always the damping term for both the configurations even in the absence of the non-aerodynamic frictional force from, for example, the axis of rotation. The argument using the index of a closed curve in the phase portrait seems to support the non-existence of periodic solution.