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Dynamics of a Chain of Coupled Pendulums
A row of pendulums coupled by torsion springs hangs from a common axis. In the continuum limit, the corresponding system of nonlinear differential equations approaches the sine-Gordon equation, whose solutions can exhibit solitons.
Contributed by:
Enrique Zeleny
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The system of nonlinear coupled differential equations derived from the Hamiltonian is
, where
and
is the moment of inertia,
is a torsion constant,
is the mass,
is the gravitational acceleration, and
is the length of the pendulums.
Reference
[1] T. Dauxois, M. Peyrard,
Physics of Solitons
, New York: Cambridge University Press, 2006 pp. 42–44.
RELATED LINKS
Gravitational Acceleration
(
ScienceWorld
)
Hamiltonian
(
ScienceWorld
)
Moment of Inertia
(
ScienceWorld
)
Pendulum
(
ScienceWorld
)
Sine–Gordon Equation
(
Wolfram
MathWorld
)
Soliton
(
Wolfram
MathWorld
)
System of Pendulums: A Realization of the Sine–Gordon Model
(
Wolfram Demonstrations Project
)
Torsion
(
ScienceWorld
)
PERMANENT CITATION
Enrique Zeleny
"
Dynamics of a Chain of Coupled Pendulums
"
http://demonstrations.wolfram.com/DynamicsOfAChainOfCoupledPendulums/
Wolfram Demonstrations Project
Published: April 22, 2013
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