The dynamics of a damped pendulum driven by a constant torque is studied experimentally and theoretically. We use this simple device to demonstrate some generic dynamical behavior including the loss of equilibrium or saddle node bifurcation with or without hysteresis and the homoclinic bifurcation. A qualitative analysis is developed to emphasize the role of two dimensionless parameters corresponding to damping and forcing.
REFERENCES
1.
J. F.
Padday
and A. R.
Pitt
, “The stability of axisymmetric menisci
,” Philos. Trans. R. Soc. London, Ser. A
275
, 489
–528
(1973
).2.
A.
Andronov
, A.
Vitt
, and S.
Khaikin
, Theory of Oscillators
(Pergamon
, New York, 1966
).3.
J. J.
Stoker
, Nonlinear Vibrations in Mechanical and Electrical Systems
(Interscience
, New York, 1950
).4.
M.
Levi
, F. C.
Hoppensteadt
, and W. L.
Miranker
, “Dynamics of the Josephson junction
,” Q. Appl. Math.
36
, 167
–198
(1978
).5.
R.
Feynman
, R.
Leighton
, and M.
Sands
, The Feynman Lectures on Physics
(Addison-Wesley
, Reading, 1963
), Vol. 2
.6.
P.
Gaspard
, “Measurement of the instability rate of a far-from-equilibrium steady state at an infinite period bifurcation
,” J. Phys. Chem.
94
, 1
–3
(1990
).7.
L.
Quartier
, B.
Andreotti
, S.
Douady
, and A.
Daerr
, “Dynamics of a grain on a sandpile model
,” Phys. Rev. E
62
, 8299
–8307
(2000
).8.
The kinetic energy of the falling ball is , where is the position of the ball in the curvilinear coordinates along the potential.
© 2005 American Association of Physics Teachers.
2005
American Association of Physics Teachers
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