Equilibrium search algorithm of a perturbed quasi-integrable system: NAFFO: Numerical Algorithm For Forced Oscillations

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Abstract

We hereby introduce and study an algorithm able to search for initial conditions corresponding to orbits presenting forced oscillations terms only, namely to completely remove the free or proper oscillating part, hereby named Namur Algorithm For Forced Oscillations, NAFFO for short. NAFFO is based on the Numerical Analysis of the Fundamental Frequencies algorithm by J. Laskar, for the identification of the free and forced oscillations, the former being iteratively removed from the solution by carefully choosing the initial conditions. We proved the convergence of the algorithm under suitable assumptions, satisfied in the Hamiltonian framework whenever the d'Alembert characteristic holds true. We provided two relevant applications: the spin-orbit problem and the forced prey-predator problem.
Original languageEnglish
Publication statusUnpublished - 2011

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Forced oscillation
Integrable Systems
Numerical Algorithms
Search Algorithm
Initial conditions
Orbit
Prey-predator
Fundamental Frequency
Numerical Analysis
Term

Keywords

  • Numerical method Frequency analysis Numerical computation of equilibria

Cite this

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title = "Equilibrium search algorithm of a perturbed quasi-integrable system: NAFFO: Numerical Algorithm For Forced Oscillations",
abstract = "We hereby introduce and study an algorithm able to search for initial conditions corresponding to orbits presenting forced oscillations terms only, namely to completely remove the free or proper oscillating part, hereby named Namur Algorithm For Forced Oscillations, NAFFO for short. NAFFO is based on the Numerical Analysis of the Fundamental Frequencies algorithm by J. Laskar, for the identification of the free and forced oscillations, the former being iteratively removed from the solution by carefully choosing the initial conditions. We proved the convergence of the algorithm under suitable assumptions, satisfied in the Hamiltonian framework whenever the d'Alembert characteristic holds true. We provided two relevant applications: the spin-orbit problem and the forced prey-predator problem.",
keywords = "Numerical method Frequency analysis Numerical computation of equilibria",
author = "Beno{\^i}t Noyelles and Nicolas Delsate and Timoteo Carletti",
year = "2011",
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AU - Noyelles, Benoît

AU - Delsate, Nicolas

AU - Carletti, Timoteo

PY - 2011

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N2 - We hereby introduce and study an algorithm able to search for initial conditions corresponding to orbits presenting forced oscillations terms only, namely to completely remove the free or proper oscillating part, hereby named Namur Algorithm For Forced Oscillations, NAFFO for short. NAFFO is based on the Numerical Analysis of the Fundamental Frequencies algorithm by J. Laskar, for the identification of the free and forced oscillations, the former being iteratively removed from the solution by carefully choosing the initial conditions. We proved the convergence of the algorithm under suitable assumptions, satisfied in the Hamiltonian framework whenever the d'Alembert characteristic holds true. We provided two relevant applications: the spin-orbit problem and the forced prey-predator problem.

AB - We hereby introduce and study an algorithm able to search for initial conditions corresponding to orbits presenting forced oscillations terms only, namely to completely remove the free or proper oscillating part, hereby named Namur Algorithm For Forced Oscillations, NAFFO for short. NAFFO is based on the Numerical Analysis of the Fundamental Frequencies algorithm by J. Laskar, for the identification of the free and forced oscillations, the former being iteratively removed from the solution by carefully choosing the initial conditions. We proved the convergence of the algorithm under suitable assumptions, satisfied in the Hamiltonian framework whenever the d'Alembert characteristic holds true. We provided two relevant applications: the spin-orbit problem and the forced prey-predator problem.

KW - Numerical method Frequency analysis Numerical computation of equilibria

M3 - Working paper

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