Editing Nonholonomic system (section)

===Linear polarized light in an optical fiber===
Take a length of optical fiber, say three meters, and lay it out in an absolutely straight line.  When a vertically polarized beam is introduced at one end, it emerges from the other end, still polarized in the vertical direction.  Mark the top of the fiber with a stripe, corresponding with the orientation of the vertical polarization.

Now, coil the fiber tightly around a cylinder ten centimeters in diameter.  The path of the fiber now describes a [[helix]] which, like the circle, has constant [[curvature]].  The helix also has the interesting property of having constant [[torsion of a curve#Properties|torsion]].  As such the result is a gradual rotation of the fiber about the fiber's axis as the fiber's centerline progresses along the helix.  Correspondingly, the stripe also twists about the axis of the helix.

When linearly polarized light is again introduced at one end, with the orientation of the polarization aligned with the stripe, it will, in general, emerge as linear polarized light aligned not with the stripe, but at some fixed angle to the stripe, dependent upon the length of the fiber, and the pitch and radius of the helix.  This system is also nonholonomic, for we can easily coil the fiber down in a second helix and align the ends, returning the light to its point of origin.  The anholonomy is therefore represented by the deviation of the angle of polarization with each circuit of the fiber.  By suitable adjustment of the parameters, it is clear that any possible angular state can be produced.