tjbetter / parallel_transport

Python and matlab scripts to animate "Moving frames, parallel transport and the geometric phase."

Moving frames and parallel transport

Parallel transport and the geometric phase

Python and matlab scripts to animate the moving frames:

• the tangent frame
• the darboux frame, and
• the frenet serret frame

and the parallel transport of a tangent vector, using the quaternions cited in reference 1).

Also animated are:

• the parallel transport of a 3-vector, and
• the geometric phase of a 2-vector.

The geometric phase is generalized to non-spherical surfaces. Surface options are:

• the 2-sphere, and
• bushings surfaces of revolution

Surfaces

References

• Brian O'Sullivan, ”The Hopf Fibration and Hidden Variables in Quantum and Classical Mechanics” April (2021) arXiv:1601.02569

• Bushings function (repository)