Nonlinear oscillation modes of double pendulum

Abstract

Abstract The article investigates nonlinear oscillations of the double mathematical pendulum having identical parameters of its links and end loads. Approximate solutions in the nonlinear zone are constructed and analyzed on the basis of exact solution in the linear zone. These solutions clearly illustrate the drift of frequencies and modes of double pendulum with increasing oscillation amplitudes. The obtained analytical results are very useful for the synthesis of controlled movement modes of wide range of manipulators and various robotic structures, and they are also necessary for constructing optimal locomotion modes of walking machines and mechanisms. These solutions are also interesting as illustrative examples of nonlinear mechanics in the teaching and engineering practice.