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