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.
PACS numbers: 02.40.-k, 05.45.-a, 45.10.Db, 45.20.Jj
Keywords: Classical mechanics, Variational principles, Averaged Lagrangian, Elastic Pendulum, Nonlinear Resonance.