Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984apj...283..316b&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 283, Aug. 1, 1984, p. 316-320.
Astronomy and Astrophysics
Astrophysics
Asymptotic Methods, Iterative Solution, Stellar Models, Stellar Oscillations, Adiabatic Conditions, Amplitude Distribution Analysis, Harmonic Oscillation, Nonadiabatic Conditions, Nonlinear Equations, Resonance
Scientific paper
An attempt to define a mathematical formalism for computing the periodic or multiperiodic oscillations of a weakly nonlinear oscillator is presented. Attention is focused on iterative theory (IT), i.e., the method of harmonic balances, applied to radial pulsators. The IT is shown capable of predicting adiabatic oscillations correctly, provided modifications are introduced to avoid divergences due to internal resonance. Chaotic solutions are, however, not amenable to IT asymptotic perturbation models. The IT is also extended to the nonadiabatic case through the addition of a work integral. The technique is demonstrated to be effective in the case of two incommensurate resonance modes in a stellar evolutionary scenario.
Buchler Jean-Robert
Pesnell William Dean
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