Title

A Numerical, Literal, and Converged Perturbation Algorithm

Document Type

Article

Publication Date

9-2017

Abstract

The KAM theorem and von Ziepel’s method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory.

Comments

Published by Springer as a work of the U.S. Federal government. Its text is subject to foreign copyright protection.

© American Astronautical Society (Outside the U.S.) 2017

The "Link to Full Text" on this page loads the PDF of the work, furnished through the Springer Nature online portal.

DOI

10.1007/s40295-016-0112-2

Source Publication

Journal of the Astronautical Sciences

Share

COinS