Periodic traveling and standing waves in a circular chain of coupled pendula and Newton's cradle

The existence of periodic traveling and standing waves for a chain of coupled pendula with periodic boundary conditions is investigated. The bifurcation arguments are achieved by applying topological methods to appropriate subspaces of symmetric solutions. The main advantage of this approach comes from the fact that only the properties of the linearized forces are required, which allows to cover a wide range of models such as Newton's cradle, the Fermi-Pasta-Ulam lattice and the Toda lattice.