What has not (yet) been understood Latest Change 2023-06-12
Some aspects of the Foucault Pendulum which I have not(yet)
understood, for which I have not(yet) found a satisfying explanation,
for which different sources in the literature give different or sometimes
Also, in my data processing I have room for improvement on the subject of fitting a dataset to an ellipse.
I present the problems in the form of study tasks.
derives that when a repelling impulse is given at a certain moment in
the pendulum's period that the precession of the ellipse (not the ellipse
itself) will be perfectly suppressed.
- Check the derivation of Schumacher, make a description of all
steps-in-between, such that a less matematically trained person also
can follow it.
- Check that the neglections which S. applies are justifyable and
- Predict what happens if the impulse is to early or to late, or to strong or to weak.
- In my spreadsheet
is a section for the Schumacher calculation where manual iteration
should be done. Try to automate that iteration process, or better, make
it superfluous by making a direct derivation.
Note: My experiments so far tend to confirm the Schumacher Criterium.
Obeying the condition I found that the Foucault Precession was reasonably
regular although there was a substantial ellipse which periodically
both attracting and repelling drive with the argument that it would
eliminate effects of certain asymmetries in the setup. However he
hardly explains which asymmetries these are.
Note that Schumacher
has some comment on this.
- Give a mathematical derivation that the story about the center magnet is
- Indicate what happens when the magnet is to weak/far off
or to strong/close by
Indicate/derive which asymetries can be suppressed by the combination
of attracting and repelling drive and indicate what happens if the
attracting and repelling impulses are not equal.
a repelling drive to counteract the forming of an ellipse. T.m.h.o. his
figure 3 indicates just the opposite (Or I do not understand it)
- Explain that Sz is right / wrong with his argument in favour of
magnet in the center:
Crane recommends a
repelling magnet in the center to eliminate the precession of the elipse,
Intuitively it feels that an attracting magnet in the center will reduce
the amount of ellipse. After all, when the Bob passes straight over it
will not have a net effect, because the effect of the atracting force
will be cancelled by that of the repelling force after the pass.
However, if there is an ellipse, there will always be an
attracting force towards the center.
The contra is: If it is so simple, why is it not done always?
- Explain whether or not a permanent magnet in the center of the base
unit will reduce the ellipticity. The Bob does have a permanent magnet
in the lowest central position.
- Explain what will happen when the magnet is to strong or to weak or has the wrong polarity.
Kamerlingh-Onnes has mayhematically derived this periodial change in
direction, but my knowledge of math is insufficient to follof his
- Explain why the ellips periodically changes direction using the simplest math.
- Explain why the changes occur when the pendulum swings East-West or North-South.
- Explain why the amplitude of the short axis varies more like a
squarewave than like a sinewave. That is, when it changes it does so
quite rapidly, within a few minutes. Is this real or is it an errort in
the way the amplitude is determined in the software I use?
(If you want to study this problem I 'll be happy to provide the necessary information).
Fitting a dataset to an ellipse.
In my dataprocessing I use a rather rude method to derive the ellips
parameters (long axis, short axis, angle of long axis and direction) from a set of
There may be a beter way.
Produce an algorithm, preferably in C or Pascal that:
Given a array of co-ordinate pairs (x, y), assumed they lay on the
circumference of an ellipse with some small measurement errors,
calculates the long axis, the short axis, the angle of the long axis
horizontal and the direction in which the elliptical path goes.
The long axis of the ellipse can have any direction 0 ..
pi. Angles > pi are not distinguishable from angles < pi. The
short axis will never be as long as the long axis
(circle). The data in the array always starts near the center, immediately after a centerpass has been detected.
Make the pendulum swing time independent of the amplitude.
It is known that the period of a pendulum depends slightly on the amplitude, even for very small amplitudes.
With my backgound as electronic engineer i am familiar with the figures
of Lissajous, a.o. an ellipse, if you plot two sine shaped signals of
the same frequency on an
X-Y oscilloscope. The shape and orientation of the ellipse depend on the
phase of the two signals. If they have exacly the same
frequency the ellipse will be stable. If the frequency of the signals
slightly differs the ellipse will change shape and orientation in a
My feeling is that the precession of the Foucault Pendulum's ellipse is
connected to the difference in swingtime between the long and short
axis' of the ellipse.
Christian Hiygens made the period of his pendulum clocks nearly
independent of the amplitude by clamping the top of the "wire" between
two cycloidally shaped brackets. The cyclo´d is known to have this
property for a pendulum with a specific length.
The question is: If we make the swing time of our pendulum independent of the amplitude, will the ellipse precession disapear?
The Huiygens trick can be applied using a properly shaped tube around the pivoting poin.t (kind of trumpet shape).
The contra is that the formula for the ellipse precession tells me that
the precession increases with a larger short-axis. This is contray to
the thought where the difference between the short- and long axis'
swingtimes is responsible for the precession. In that case we should see
less precession when the swingtimes are closer to each other.
Pull me out of this swamp.