Parallel Transport and Precession Simulation
(The geodesic flux of precession is generated by the spin axis loop holonomy proportional to the enclosed area) Bernd Binder, 30.11.2008

Change the modes (drag, rotate, draw, lift) in the drop-down list below on the right to experience parallel transport and precession using the mouse bottons on the sphere. (If it won't start, check security settings or download the Java runtime here from Sun).
The applet is written using Java. You must have a Java enabled browser to be able to see this applet. Users of the Microsoft Internet Explorer should check their Java options or download the Java runtime here from Sun.
This applet is based on the "EggMath" school tutorial, created by Professors Steve Bradlow (UIUC) and John Sullivan (TU Berlin) Math Departments.

Taking an arrow representing a tangential vector and moving it on a closed loop on the surface of a sphere according to the applet, we get a rotation of the arrow by an holonomy angle visualizing the holonomy effect, which is obtained from the concept of parallel transport. The kinematic way of understanding parallel transport on the sphere applies equally well to any closed surface. Precession is given by holonomic rotation angle, which is the area (of the sphere or triangle) enclosed by the precessing spin vector loop (divided by r^2). Magic Angle Precession (MAP) arises from a radial variation of the radial distance with constant holonomy flux (triangle area according to Gauss law), which is a gauge potential representing electric charge, where magnetic effects arise from extra rotations under SO(3).

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(c) Bernd Binder 2002-2008