Equilibrium states of an inverted pendulum acted upon by a follower force on the elastically restrained upper end

A model of an elastic beam subjected to a follower force represented by an inverted two-link pendulum with elastoviscous joints is studied. It is shown that a divergent bifurcation can occur at certain values of the magnitude of the follower force and stiffness of the elastic restraint. As a result of this bifurcation, the vertical equilibrium becomes unstable and two new non-vertical equilibrium states appear. This bifurcation is referred to as the fork bifurcation or triple equilibrium bifurcation.