Stepwise Precession of the Resonant Swinging Spring

Stepwise Precession of the Resonant Swinging Spring

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 wellknown 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 thi...

Pulsation and Precession of the Resonant Swinging Spring

When the frequencies of the elastic and pendular oscillations of an elastic pendulum or swinging spring are in the ratio two-to-one, there is a regular exchange of energy between the two modes of oscillation. We refer to this phenomenon as pulsation. Between the horizontal excursions, or pulses, the spring undergoes a change of azimuth which we call the precession angle. The pulsation and stepw...

Stepwise Pre ession of the Resonant Swinging Spring

Resonant Rossby Wave Triads and the Swinging Spring

From page xxxx) The wave solutions discovered by Rossby are of fundamental importance for atmospheric dynamics. The nonlinear interactions between these waves determine the primary characteristics of the energy spectrum. These interactions take place between triplets of waves known as “resonant triads” and, for small amplitude, they are described by the three-wave equations. These same equation...

The Swinging Spring : A Simple