Figure 22.19.1 (See in context.)

Figure 22.19.1: Jacobi’s amplitude function for and . When , increases monotonically indicating that the motion of the pendulum is unbounded in , corresponding to free rotation about the fulcrum; compare Figure 22.16.1. As , plateaus are seen as the motion approaches the separatrix where , , at which points the motion is time independent for . This corresponds to the pendulum being “upside down” at a point of unstable equilibrium. For , the motion is periodic in , corresponding to bounded oscillatory motion.