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Articles and sites about theory and practice of the Foucault pendulum.

The Dutch physicist Heike Kamerlingh Onnes (yes, the one from the liquid Helium and the superconductivity) had his doctoral thesis in 1879 about the Foucault pendulum.
His thesis (download) (in Dutch. I do not know about an English translation, there seems to exist a German version) contains besides comprehensive math about the ellipse problem, a description and drawings of his rather short pendulum, which had some very smart details.
The title of his thesis is (translated) "New evidence for the axial rotation of the Earth".
Source: www.lorentz.leidenuniv.nl/history/proefschriften/sources/Kamerlingh_Onnes_1879.pdf.
My knowledge of math is far insufficient to follow his formulas, but I can read the text inbetween.

Schulz-DuBois (download) “Foucault Pendulum Experiment by Kamerlingh Onnes and degenerated Perturbation Theory” contains a hommage to Kamerlingh-Onnes.

Cartmell et al (download) describe problems you may encounter when you try to construct an extreme precise pendulum to prove a certain relativistic effect. He also has an extensive literture list.

Crane (download)  eliminates the precession of the ellipse (not the ellipse itself) with a repelling magnet in the center. The exitation of the bob is both attracting and repelling.

Salva et al (download) describe a short pendulum with eddy current damping, and a tracking mechanism with Hall sensors.
Salva mentions E.O. Schulz-DuBois, Am. J. Phys. 88, 173 (1969) as a reference to the work of Kamerlingh Onnes. I was not able to verify this.

Lima and Arun (download) derive an accurate formula for the period of a pendulum at larger amplitudes.

Longden (download) describes some constructions for mounting a pendulum such that ellipse forming is limited. I suppose he was not aware that ellipse forming is fundamental, even with the most perfect mounting.

Roland Szostak (download)  builds a simple pendulum for schools. He indicates that repelling excitation is to be preferred over attracting, but argues that with only a simple drawing which t.m.h.o. shows the opposite.

Schumacher (download) derives that when a repelling impulse is given at the right moment, the precession due to the ellipse can be eliminated completely.
The distance d at which the impulse should be given depends only on the Length, the Amplitude and the Q-factor of the pendulum. It turns out that the higher the Q-factor is, the earlier the drive pulse should be given.
My experiments up to now tend to confirm this. In all pendulums I operated up to now I've seen alternating ellipses, changing direction around E-W and around N-S. When the impulse is given to early the ellipse precession is overcompensated, that is, during a CCW ellipse the precession goes CW and during a CW ellipse the precession goes CCW. When the kick is given to late it is just the opposite.

Pippard (download) treats a driving method where the top mounting point is lifted periodically, also known as piston drive.
He also directs to his book "The physics of vibration" (download)

Haringx en Suchtelen (download) tell about the pendulum in the UN building in New York, a present from NL in 1955. Interresting is how the principle of the Charron ring is implemented there.

Salva N.N. and Salva H.H.  Interplay between Airy and Coriolis precessions in a real Foucault pendulum

Giacomo Torzo (download)describes the pendulum in Padova (it). There is also a nice youtube video and an interview with Giacomo (Italian spoken).

Walter Lewin (video)  demonstrates in his last college that the period of a pendulum is dependent on the amplitude, but not on the mass of the bob. He himself takes the role of bob and he can draw beautiful dotted lines on the blackboard. There are some other physics experiments too.

Professor Kielkopf describes a lot of details of the pendulum in the University of Louisville, (download) KY, USA

Franz Kraft has made a demo of the orbits a foucault pendulum can follow in the Wolfram programming language..

Witzel (link) describes a short pendulum with piston drive and an attracting magnet to counteract ellipse forming.

A manufacturer of Foucault pendulums (link) has several manuals on the site. These reveil quite some information about the construction and operation.

Vereault: Anisosphere Analysis of Foucault pendulum vs Torsion pendulum.(download)

Vereault, Tremblay: Damping and Suspension Anisotropy (download)

Vereault, Anisosphere as a new tool   (contains work of Kamerlingh-Onnes)  (download)

Vereault: Tidal accelerations and dynamical properties of 3-df pendula.  (download)

A site about other effects of the rotation of the earth. (link)

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Oh yes...  I also found  Sheng Wang et al (download) who invented "new physics" to explain certain behaviour of a foucault pendulum.
It looks like the "Ether" theory is back and now called "No-Shape-Substance" ?????

A U.S. patent describes how to get 250 kW on free energy from the precession of a foucault pendulum.