Saddle transport and chaos in the double pendulum

Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical theory. In particular, the double pendulum is a prototypical chaotic system frequently used to illustrate variety phenomena in nonlinear dynamics. this work, we explore existence implications codimension-1 invariant manifolds pendulum, which originate from unstable periodic orbits around saddle equilibria act as separatrices mediate global phase space transport. Motivated part by similar studies on three-body problem, able draw direct comparison between dynamics transport solar system, exist vastly different scales. Thus, may be viewed table-top benchmark chaotic, saddle-mediated transport, with relevance energy-efficient mission design. The analytical results work provide an result, concerning arbitrarily long itineraries space, applicable wide class two degree freedom Hamiltonian systems, including problem pendulum. This manuscript details corresponding acrobatic motions can identified controlled laboratory setting.