Lyapunov instability of pendulums, chains, and strings

We investigate both dynamic and time-averaged chaos in a series of problems ranging from a simple pendulum to many-body chains and strings of particles in a gravitational field. Chain and spring systems typically display time-averaged Lyapunov spectra resembling those of one- and two-dimensional statistical-mechanical systems, but with details depending strongly on the nature of the links and the choice of canonical coordinates.