Special points in projections on the plane of the coordinate of the Northern pole of the Earth

In this paper, we discuss the possibility and conditions for the emergence of singularities in projections onto the plane of the daily coordinates of the Earth’s North Pole. Singular points on the graphs of the positions of the instantaneous pole of the Earth are considered as geometric shapes of projection on the plane of the smooth (quasiperiodic) process of motion of the instantaneous pole on the Earth’s surface with a certain ratio between the values of the external control parameters and the internal ones that determine the rotation of the Earth around its axis. The emergence of singular points is the result of a certain physical rearrangement in the oscillating system of the Earth and the geomagnetic field and atmosphere associated with it by the energy exchange processes.