Abstract: The spherical pendulum is a single pendulum that rotates around the suspension point under the action of gravity, and hence its center of mass is constrained on a sphere. In this paper, we numerically simulate the motion of a single spherical pendulum, and discuss the dependence of the swing period on the initial conditions. By the numerical analysis of the dynamics of the coupled spherical pendulums, we show the influence of the spring stiffness on the energy transfer, discuss the frequency distribution of the energy, and clarify the chaotic state of the nonlinear large swing angle motion.

Key words: spherical pendulum, coupled pendulums, Fourier transform, nonlinear dynamics