Foucault Pendulum - Related Physical Systems

Related Physical Systems

There are many physical systems that precess in a similar manner to a Foucault pendulum. As early as 1836, Edward Sang contrived and explained the precession of a spinning top link. In 1851, Charles Wheatstone described an apparatus that consists of a vibrating spring that is mounted on top of a disk so that it makes a fixed angle with the disk. The spring is struck so that it oscillates in a plane. When the disk is turned, the plane of oscillation changes just like the one of a Foucault pendulum at latitude .

Similarly, consider a non-spinning perfectly balanced bicycle wheel mounted on a disk so that its axis of rotation makes an angle with the disk. When the disk undergoes a full clockwise revolution, the bicycle wheel will not return to its original position, but will have undergone a net rotation of .

Another system behaving like a Foucault pendulum is a South Pointing Chariot that is run along a circle of fixed latitude on a globe. If the globe is not rotating in an inertial frame, the pointer on top of the chariot will indicate the direction of swing of a Foucault pendulum that is traversing this latitude.

Spin of a relativistic particle moving in a circular orbit precesses similar to the swing plane of Foucault pendulum. The relativistic velocity space in Minkowski spacetime can be treated as a sphere S3 in 4-dimensional Euclidean space with imaginary radius and imaginary timelike coordinate. Parallel transport of polarization vectors along such sphere gives rise to Thomas precession, which is analogous to the rotation of the swing plane of Foucault pendulum due to parallel transport along a sphere S2 in 3-dimensional Euclidean space.

In physics, the evolution of such systems is determined by geometric phases. Mathematically they are understood through parallel transport.