The Hannay geometric phase is the classical analog of the well-known Berry phase. Its most familiar example is the effect of the latitude λ on the motion of a Foucault pendulum. We describe an electronic network whose behavior is exactly equivalent to that of the pendulum. The circuit can be constructed from off-the-shelf components using two matched transconductance amplifiers that comprise a gyrator to introduce the non-reciprocal behavior needed to mimic the pendulum. One may precisely measure the dependence of the Hannay phase on λ by circuit simulation and by laboratory measurements on a constructed circuit.

1.
M. V.
Berry
, “
Quantal phase factors accompanying adiabatic changes
,”
Proc. R. Soc. London, Ser. A
392
(
1802
),
45
57
(
1984
).
2.
S.
Pancharatnam
, “Generalized theory of interference and its applications. Part I. Coherent pencils,”
Proc. Ind. Acad. Sci. A
44
,
247
(
1956
). [reprinted in S. Pancharatnam, Collected Works (Oxford University Press, 1975)].
3.
J. H.
Hannay
, “
Angle variable holonomy in adiabatic excursion of an integrable Hamiltonian
,”
J. Phys. A
18
,
221
(
1985
).
4.
For a very recent visit to the pendulum see for example:
J. A.
Giacometti
, “
Foucault pendulum revisited, the determination of precession angular velocity using Cartesian coordinates
,”
Rev. Bras. Ensino Fis.
43
,
e20190140
(
2021
).
5.
A.
Khein
and
D. F.
Nelson
, “
Hannay angle study of the Foucault pendulum in action-angle variables
”,
Am. J. Phys.
61
,
170
(
1993
).
6.
D.
Xu
, “
Hannay angle in an LCR circuit with time-dependent inductance, capacity and resistance
,”
J. Phys. A
35
,
L455
(
2002
).
7.
J. H.
Hannay
, “
Comment on Hannay angle in an LCR circuit with time-dependent inductance, capacity and resistance
,”
J. Phys. A
35
,
9699
(
2002
).
8.
Sharba
Bhattacharjee
 et al, “
Study of geometric phase using classical coupled oscillators
,”
Eur. J. Phys.
39
,
035404
(
2018
).
9.
A. D. A. M.
Spallicci
, “
Satellite measurement of the Hannay angle
,”
Nuovo Cimento B
119
,
1215
(
2004
).
10.
J. B.
Marion
,
Classical Dynamics of Particles and Systems
(
Elsevier
,
New York
,
2014
).
11.
W. B.
Somerville
, “
The description of Foucault's pendulum
,”
Q. J. R. Astron. Soc.
13
,
40
62
(
1972
).
12.
J.
von Bergmann
, “
Foucault pendulum through basic geometry
,”
Am. J. Phys.
75
,
888
892
(
2007
).
13.
M.
Caruso
,
H.
Fanchiotti
,
C. A.
Garcia Canal
,
M.
Mayosky
, and
A.
Veiga
, “
The quantum CP-violating kaon system reproduced in the electronic laboratory
,”
Proc. R. Soc. London, Ser. A
472
(
2195
),
20160615
(
2016
).
14.
See supplementary material at https://www.scitation.org/doi/suppl/10.1119/5.0081149 for a description of the elements of the experimental circuit, their calibration procedure, the proposed initial conditions for a better visualization and the measurement procedure.
15.
I.
Tatai
and
I.
Zaharie
, “
The energy transfer between the ports of an implemented gyrator using LM13700 operational transconductance amplifier
,”
Rev. Sci. Instrum.
83
(
11
),
114702
(
2012
).

Supplementary Material

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