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.

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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.
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