KAM Tori Construction Algorithms

Abstract

In this paper we evaluate and compare two algorithms for the calculation of KAM tori in Hamiltonian systems. The direct fitting of a torus Fourier series to a numerically integrated trajectory is the first method, while an accelerated finite Fourier transform is the second method. The finite Fourier transform, with Hanning window functions, is by far superior in both computational loading and numerical accuracy. Some thoughts on applications of KAM tori are offered.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 2008
Accession Number
ADA532040

Entities

People

  • William E. Wiesel

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Algorithms
  • Amplitude
  • Construction
  • Equations
  • Equations Of Motion
  • Errors
  • Fourier Series
  • Frequency
  • Numerical Integration
  • Orbits
  • Periodic Functions
  • Perturbation Theory
  • Spectral Lines
  • Time Intervals
  • Trajectories

Readers

  • Computational Modeling and Simulation
  • Wave Propagation and Nonlinear Chaotic Dynamics.