On the dynamics of spring-pendulum system: an overview of configuration space and phase space

Abstract

The dynamics of the spring-pendulum system with two degrees of freedom were studied. The motion of this system is restricted to be in a vertical plane so that the chosen generalized coordinates are the increased length of the spring  and the swing angle of pendulum . Hamiltonian of the system is obtained from the Legendre transformation of Lagrangian. Hamilton’s equation yields four differential equations that represent the dynamic of the system. The obtained results were visualized in configuration space and phase space trajectories. It is shown that generally the greater the initial swing angle, the more complex pattern will occur followed by the appearance of chaotic phenomena.