Traveling and standing waves in coupled pendula and Newton's cradle

TL;DR

This paper investigates traveling and standing waves in chains of coupled pendula and similar models, using topological methods that rely only on linearized force properties, applicable to various systems.

Contribution

It introduces a topological approach to prove the existence of waves in coupled systems, applicable to models like Newton's cradle and Fermi-Pasta-Ulam lattice.

Findings

Existence of traveling and standing waves established.

Applicable to a wide range of coupled systems.

Method relies only on linearized force properties.

Abstract

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