In this second article on hamiltonian systems, we present the blow-up method for the determination of the nature of degenerate fixed points (equilibrium points). We apply the method to two hamiltonian models with one and two degrees of freedom respectively. Firstly we study a system formed by a simple pendulum subjected to a constant external torque. Then we consider a system formed by a double pendulum of segments with equal lengths and masses, also subjected to nonvanishing constant external torques. The presence of degenerate equilibrium points in both cases of simple and double pendulums occurs for some values of the external torques.
degenerate equilibrium points; blow-up method; hamiltonian systems