Method of Generating N-dimensional Isochronous Nonsingular Hamiltonian Systems

DOI

10.1080/14029251.2013.792474How to use a DOI?

Abstract

In this paper we develop a straightforward procedure to construct higher dimensional isochronous Hamiltonian systems. We first show that a class of singular Hamiltonian systems obtained through the Ω-modified procedure is equivalent to constrained Newtonian systems. Even though such systems admit isochronous oscillations, they are effectively one degree of freedom systems due to the constraints. Then we generalize the procedure in terms of Ω_i -modified Hamiltonians and identify suitable canonically conjugate coordinates such that the constructed Ω_i -modified Hamiltonian is nonsingular and the corresponding Newton's equation of motion is constraint free. The procedure is first illustrated for two dimensional systems and subsequently extended to N-dimensional systems. The general solution of these systems are obtained by integrating the underlying equations and is shown to admit isochronous as well as amplitude independent quasiperiodic solutions depending on the choice of parameters.

Copyright

© 2013 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

TY  - JOUR
AU  - A. Durga Devi
AU  - R. Gladwin Pradeep
AU  - V.K. Chandrasekar
AU  - M. Lakshmanan
PY  - 2021
DA  - 2021/01/06
TI  - Method of Generating N-dimensional Isochronous Nonsingular Hamiltonian Systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 78
EP  - 93
VL  - 20
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2013.792474
DO  - 10.1080/14029251.2013.792474
ID  - DurgaDevi2021
ER  -