A double pendulum submitted to external torques is employed to introduce some basic fundamentals of dynamical systems theory to physics undergraduate courses, soon after the student takes the analytical mechanics discipline. This system is a good example for the introduction of such techniques. Hamilton's equations of motion indicate the existence of stationary solutions (equilibrium points) in the phase space of the model. The identification of the nature of these points allows the description of the system dynamics around their linear neighborhood. Moreover, qualitative results obtained in the linear neighborhood of a fixed point are not changed by the introduction of non-vanishing constant external torques. This work emphasizes the analysis of the linear neighborhood of the equilibrium points.
hamiltonian systems; dynamical systems theory; chaos
