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The dynamics of the driven pendulum have been studied numerically and analytically under non-resonance condition, where the driving frequency is far from the characteristic frequency of the pendulum. It is found that, as is known previously, a symmetry·breaking occurs when the driving amplitude j exceeds a critical value, but further increase of j does not lead to a chaotic phase of motion, but to an inversion of the pendulum. Namely, in a definite range of j, the pendulum oscillates in the inverted configuration. The normal and inverted configurations appear alternately as j still increases. It is also found that, for intermediate values of j, at most four phases of motion (single-period as well as period-tripled oscillations, and modulated rotations in the positive or negative direction) can coexist with each other. Most of the dynamical structures obtained numeri­ cally can be explained by perturbation expansion solutions of the equation of motion.

New Dynamical Aspects of the Driven Pendulum