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.
The system of nonlinear coupled differential equations derived from the Hamiltonian is
and is the moment of inertia, is a torsion constant, is the mass, is the gravitational acceleration, and is the length of the pendulums.
 T. Dauxois, M. Peyrard, Physics of Solitons, New York: Cambridge University Press, 2006 pp. 42–44.