Dynamics of a complex mechanical pendulum : and its dependence on energy

Abstract: In this thesis we analyze the motion of the double pendulum in which the first rod has a distributed mass and the second is a light rod with a linked spring attached to a point mass. The dynamics of the system is modelled in Maple using the Sophia package and Lagrangian mechanics. Trajectories, phase portraits, conservation of energy etc. are studied to determine the systems stability for different energy levels and the models accuracy. A study of the systems properties such as its sensitivity to initial condition and denseness of orbits was done to conclude if the system exhibit chaotic motion.