EXPLANATION OF THE FOUCAULT PENDULUM BASED ON THE PARALLEL TRANSPORT OF VECTORS

The precession of the swing plane of the Foucault pendulum can be explained using either Newtonian mechanics or the parallel transport of vectors. The latter one, however, requires a profound understanding of differential geometry, making it less accessible to readers with a background in mechanics. This paper offers a geometrically intuitive explanation of the parallel transport of vectors on a curved surface, establishing its correlation with pure rolling. By applying the principle of momentum, it is proven that the velocity vector at intervals of the oscillation period of the pendulum undergoes parallel transport along a latitude on the sphere. The angular velocity of the swing plane precession is then determined through both graphical interpretation and mathematical calculation. This paper only requires readers to possess a basic understanding of vector operations and the principle of momentum, enabling them to have a deeper comprehension of the Foucault pendulum and establish the connection between mechanics and geometry.