Controlling the stability of periodic orbits of completely integrable systems

Abstract

We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed system becomes a codimension-one dissipative dynamical system which also admits that orbit as a periodic orbit, but whose stability can be a-priori prescribed. The main results are illustrated in the case of a three dimensional dissipative perturbation of the harmonic oscillator, and respectively Euler's equations form the free rigid body dynamics.

19 pages

References in corpus (3)

• Asymptotic Stability for a Class of Metriplectic Systems
• On local generators of affine distributions on Riemannian manifolds
• On the stability of periodic orbits for differential systems in ${\mathbb{R}}^n$

Cited by in corpus (1)

• Asymptotic stabilization with phase of periodic orbits of three-dimensional Hamiltonian systems