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Math. Comput. Appl. 2017, 22(3), 37; doi:10.3390/mca22030037

Analytical Solution to Normal Forms of Hamiltonian Systems

Department of Mathematics, College of Sciences, Qassim University, P.O. Box 6666, Buraydah 51452, Saudi Arabia
Received: 10 June 2017 / Revised: 12 July 2017 / Accepted: 26 July 2017 / Published: 27 July 2017
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Abstract

The idea of the normalisation of the Hamiltonian system is to simplify the system by transforming Hamiltonian canonically to an easy system. It is under symplectic conditions that the Hamiltonian is preserved under a specific transformation—the so-called Lie transformation. In this review, we will show how to compute the normal form for the Hamiltonian, including computing the general function analytically. A clear example has been studied to illustrate the normal form theory, which can be used as a guide for arbitrary problems. View Full-Text
Keywords: Hamiltonian; normal forms; generating function; Lie transformation; canonical transformation Hamiltonian; normal forms; generating function; Lie transformation; canonical transformation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Allahem, A. Analytical Solution to Normal Forms of Hamiltonian Systems. Math. Comput. Appl. 2017, 22, 37.

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