Spherical pendulum

Interactive three.js simulation with an orbitable 3D camera showing up to 12 spherical pendulums arranged in a circle, with damping and the g force displayed on demand. When N = 2, two pendulums can be compared using independent parameters (initial angle, azimuthal angular velocity, and length); when N ≠ 2, all pendulums share Pendulum 1's parameters. The simulation displays trajectories in (x,y) and (x,y,z), as well as graphs of Pendulum 1's angle and angular velocity over time or in phase space.

Unlike a planar pendulum, a spherical pendulum has two angular degrees of freedom, and for most initial conditions its trajectory does not close: the plane of oscillation slowly precesses around the vertical axis, an effect directly visible in the motion's (x, y) projection.

Marco P. M. de Souza