The Study of the Pendulum with Heavy Neo-Hookean Rod

Abstract

The present paper is a generalization of the problem of a rubber spring pendulum discussed by Bhattacharyya in 2000 and Stănescu in 2011, which studied the case of the neo-Hookean rod without mass. In our paper we consider that the mass of the neo-Hookean rod is not negligible and its deformation is realized such that at any moment of time the rod can be treated as a homogeneous rigid bar of variable length. Using the second order Lagrange equations we obtained the equations of motion in the most general case and we identified as particular cases the situations presented in the bibliography. We also performed a study of the equilibrium positions and their stability. A study of the small oscillations about the stable equilibrium positions is realized too. The theoretical results are finally compared to those obtained by numerical simulation.