11428
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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
THINGS TO TRY
Slider Zoom
Automatic Animation
SNAPSHOTS
DETAILS
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
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
System of Pendulums: A Realization of the Sine-Gordon Model
Balázs Meszéna
Blip Solitons
Roger Beresford
Pendulum with Three Magnets
Enrique Zeleny
Series Approximation for the Nonlinear Pendulum
Enrique Zeleny
Tuned Mass Damper System
Enrique Zeleny
Coupled Pendulum Oscillations
Stephen Wilkerson (Towson University)
Pendulum Waves
Stan Wagon (Macalester College) and S. M. Blinder
Vibrations of a Hanging String
Enrique Zeleny
Chaotic Dynamics of a Magnetic Pendulum
Galen Craven
Double Pendulum
Rob Morris
Related Topics
Differential Equations
Mechanics
Physics
Wavelets
Waves
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+