Аннотация:This publication is dedicated to the presentation of the fundamentals of the fundamental theory of the "generalized" Foucault pendulum, implemented based on a fundamentally new 3-D spherical resonance gyroscope, whose basic sensitive element is a high-quality hollow spherical resonator. The generalization of the Brian effect to the spatial case is considered and investigated-specifically, an elastic spherically symmetric solid body with a free boundary subjected to mass forces is examined. The planar rotation of the spherical resonator is replaced by spatial rotation. In such an experiment, the generalized effect of Brian's inertia also becomes spatially relevant.