### 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 language | English |
---|---|

Pages (from-to) | 221-230 |

Number of pages | 10 |

Journal | Celestial Mechanics and Dynamical Astronomy |

Volume | 56 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Mar 1993 |

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### Keywords

- Hamiltonian systems
- resonance

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Celestial Mechanics and Dynamical Astronomy*,

*56*(1-2), 221-230. https://doi.org/10.1007/BF00699734

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

Research output: Contribution to journal › Article

*Celestial Mechanics and Dynamical Astronomy*, vol. 56, no. 1-2, pp. 221-230. https://doi.org/10.1007/BF00699734

}

TY - JOUR

T1 - A fourth-order solution of the ideal resonance problem

AU - Érdi, B.

AU - Kovács, József

PY - 1993/3

Y1 - 1993/3

N2 - 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.

AB - 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.

KW - Hamiltonian systems

KW - resonance

UR - http://www.scopus.com/inward/record.url?scp=0141446461&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141446461&partnerID=8YFLogxK

U2 - 10.1007/BF00699734

DO - 10.1007/BF00699734

M3 - Article

AN - SCOPUS:0141446461

VL - 56

SP - 221

EP - 230

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

IS - 1-2

ER -