Stepwise Precession of the Resonant Swinging Spring

Details Stepwise Precession of the Resonant Swinging Spring Stepwise Precession of the Resonant Swinging Spring

2001-04-17

arxiv.org/abs/nlin/0104038v1

Nonlinear Sciences

Chaotic Dynamics

28 pages, 10 figures

Scientific paper

10.1137/S1111111101388571

The swinging spring, or elastic pendulum, has a 2:1:1 resonance arising at cubic order in its approximate Lagrangian. The corresponding modulation equations are the well-known three-wave equations that also apply, for example, in laser-matter interaction in a cavity. We use Hamiltonian reduction and pattern evocation techniques to derive a formula that describes the characteristic feature of this system's dynamics, namely, the stepwise precession of its azimuthal angle.

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