Method of Generating N-dimensional Isochronous Nonsingular Hamiltonian Systems
- 10.1080/14029251.2013.792474How to use a DOI?
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 Ωi -modified Hamiltonians and identify suitable canonically conjugate coordinates such that the constructed Ωi -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.
- © 2013 The Authors. Published by Atlantis Press and Taylor & Francis
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Cite this article
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 -