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The results of an analysis and comparison of times of appearance of the features of the long-term displacement of the geographic North Pole over the Earth's surface and the components of the angular momentum of the atmosphere and global jumps in the geomagnetic field are presented. The calculations used long-term data on the motion of the geographic North Pole with intervals between readings of 0.05 years, data on the components of the angular momentum of the atmosphere, and information on the appearance of global jumps observed at all magnetic observatories of the globe. The following methods were used in the study: wavelet analysis, approximation of nonlinear trends by smooth functions, and two-channel spectral analysis. Based on the results of the analysis, a conclusion was drawn about a possible connection between the features in the nonlinear trends of the motion of the geographic North Pole over the Earth's surface and the components of the angular momentum of the atmosphere, as well as global jumps in the secular variations of the geomagnetic field in the interval of 1964–1980 with global energy rearrangements in the adjacent shells of the Earth's system. Coherence was established between variations with a period of 35.3 years in data on the variation in the position of the North Pole relative to the conditional beginning and in data on the variation in the dipole moment. The possibility of the process of their synchronization with an advance of 6 years of fluctuations in data on the variation in the dipole moment is allowed. [ABSTRACT FROM AUTHOR]