A fourth-order solution of the ideal resonance problem

B. Érdi, József Kovács

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The second-order solution of the Ideal Resonance Problem, obtained by Henrard and Wauthier (1988), is developed further to fourth order applying the same method. The solutions for the critical argument and the momentum are expressed in terms of elementary functions depending on the time variable of the pendulum as independent variable. This variable is related to the original time variable through a 'Kepler-equation'. An explicit solution is given for this equation in terms of elliptic integrals and functions. The fourth-order formal solution is compared with numerical solutions obtained from direct numerical integrations of the equations of motion for two specific Hamiltonians.

Original languageEnglish
Pages (from-to)221-230
Number of pages10
JournalCelestial Mechanics and Dynamical Astronomy
Volume56
Issue number1-2
DOIs
Publication statusPublished - Mar 1993

Fingerprint

elliptic functions
pendulums
numerical integration
momentum
equations of motion
method

Keywords

  • Hamiltonian systems
  • resonance

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

A fourth-order solution of the ideal resonance problem. / Érdi, B.; Kovács, József.

In: Celestial Mechanics and Dynamical Astronomy, Vol. 56, No. 1-2, 03.1993, p. 221-230.

Research output: Contribution to journalArticle

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