Complete reduction of oscillators in resonance p:q
This paper extends to any type of resonance (p:q) the Lissajous transformation that handles the resonance (1:1) in a Hamiltonian composed of two harmonic oscillators. The manifolds of constant energy for such a system are two-dimensional surfaces of revolution that are spheres for the resonance 1:1, spheres pinched once for the resonances (1:q) when 1<q, and spheres pinched twice for the resonances (p:q) when 1<p<q. The extended Lissajous transformation is valid for resonant pseudo-oscillators (a nondefinite quadratic form), which allows us to find that the reduced phase flow lies on an unbounded surface of revolution.
Elipe
A
Grupo de Mecanica Espacial, Universidad de Zaragoza, 50009 Zaragoza, Spain.