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In Chapter 6 , we discussed small amplitude oscillations of systems with one degree of freedom. In this chapter, we consider two important conservative systems with one degree of freedomDegrees of freedom that display oscillationsOscillations that are not necessarily of small amplitude: the simple pendulumPendulumsimple and the anharmonic oscillatorOscillatoranharmonic. The first qualitative change is that the period of oscillations becomes amplitude-dependent. Unlike those of a harmonic oscillatorOscillatorharmonic, Hamilton’s equationsHamilton’sequations of motion here are nonlinear. This means the associated Hamiltonian vector fieldVector fieldHamiltonian on phase space has components that are nonlinear functions of the coordinates on phase space.

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Nonlinear Oscillations: Pendulum and Anharmonic Oscillator

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  • 发表日期：

    2025年

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  • Govind S. Krishnaswami

摘要

In Chapter 6 , we discussed small amplitude oscillations of systems with one degree of freedom. In this chapter, we consider two important conservative systems with one degree of freedomDegrees of freedom that display oscillationsOscillations that are not necessarily of small amplitude: the simple pendulumPendulumsimple and the anharmonic oscillatorOscillatoranharmonic. The first qualitative change is that the period of oscillations becomes amplitude-dependent. Unlike those of a harmonic oscillatorOscillatorharmonic, Hamilton’s equationsHamilton’sequations of motion here are nonlinear. This means the associated Hamiltonian vector fieldVector fieldHamiltonian on phase space has components that are nonlinear functions of the coordinates on phase space.