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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)