Asymptotic stabilization with phase of periodic orbits of three-dimensional Hamiltonian systems
Dynamical Systems
2017-09-14 v3 Mathematical Physics
math.MP
Abstract
We provide a geometric method to stabilize asymptotically with phase an arbitrary fixed periodic orbit of a locally generic three-dimensional Hamiltonian dynamical system. The main advantage of this method is that one needs not know a parameterization of the orbit to be stabilized, but only the values of the Hamiltonian and a fixed Casimir (of the Poisson configuration manifold) at that orbit. The stabilization procedure is illustrated in the case of the Rikitake model of geomagnetic reversal.
Keywords
Cite
@article{arxiv.1506.02144,
title = {Asymptotic stabilization with phase of periodic orbits of three-dimensional Hamiltonian systems},
author = {Razvan M. Tudoran},
journal= {arXiv preprint arXiv:1506.02144},
year = {2017}
}
Comments
17 pages