What is the connection between the Foucault pendulum and parallel transport?

Question

I try to explain the Foucault pendulum with the concept of parallel transport(if we think of Earth as being a perfect sphere) but I can't quite figure out what the vector that gets parallel transported represents(for example, is it the normal to the plane of oscillation vector?).

In particular, I can't exaplain the following animation https://en.wikipedia.org/wiki/File:Foucault_pendulum_plane_of_swing_semi3D.gif
which is found in this wikipedia article
https://en.wikipedia.org/wiki/Foucault_pendulum
using the concept of parallel transport.

Related : What is the drawing scheme of the parallel transport of a vector?. — Frobenius, Sep 08 '21 at 10:44
The animation on Wikipedia shows the parallel transport along a circle of constant lattitude (30 degrees north in this case) of a tangent vector that rotates continuously in its tangent plane. In the case shown, a 2 \pi rotation of the tangent vector takes exactly two loops around the path. At any instant, this tangent vector is tangent to the plane of the pendulum. — Praan, Jul 22 '23 at 19:38

score 0 · Answer 1 · answered Sep 08 '21 at 10:18

0

The in-plane vector represents the pendulum swing-plane. This is why the pendulum appears to rotate as it traverses a path on the sphere (ie, as earth rotates).

Here's a good reference: https://www.maa.org/sites/default/files/pdf/upload_library/1/1/Oprea-Ford-1996.pdf

answered Sep 08 '21 at 10:18

guest

1

While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. – Sebastiano Sep 08 '21 at 12:21

What is the connection between the Foucault pendulum and parallel transport?

1 Answers1