Standard

The Expansion of the Hamiltonian of the Planetary Problem into the Poisson Series in All Keplerian Elements (Theory). / Kholshevnikov, K.; Greb, Alexandr V.; Kuznetsov, E. d.
In: Solar System Research, Vol. 35, No. 3, 2001, p. 243-248.

Research output: Contribution to journal › Article › peer-review

Harvard

Kholshevnikov, K, Greb, AV & Kuznetsov, ED 2001, 'The Expansion of the Hamiltonian of the Planetary Problem into the Poisson Series in All Keplerian Elements (Theory)', Solar System Research, vol. 35, no. 3, pp. 243-248. https://doi.org/10.1023/A:1010487107989

APA

Kholshevnikov, K., Greb, A. V., & Kuznetsov, E. D. (2001). The Expansion of the Hamiltonian of the Planetary Problem into the Poisson Series in All Keplerian Elements (Theory). Solar System Research, 35(3), 243-248. https://doi.org/10.1023/A:1010487107989

Vancouver

Kholshevnikov K, Greb AV, Kuznetsov ED. The Expansion of the Hamiltonian of the Planetary Problem into the Poisson Series in All Keplerian Elements (Theory). Solar System Research. 2001;35(3):243-248. doi: 10.1023/A:1010487107989

Author

Kholshevnikov, K. ; Greb, Alexandr V. ; Kuznetsov, E. d. / The Expansion of the Hamiltonian of the Planetary Problem into the Poisson Series in All Keplerian Elements (Theory). In: Solar System Research. 2001 ; Vol. 35, No. 3. pp. 243-248.

BibTeX

@article{f6b691a2231e4ead86ebbfda31c9df4c,
title = "The Expansion of the Hamiltonian of the Planetary Problem into the Poisson Series in All Keplerian Elements (Theory)",
abstract = "The study of the evolution of planetary systems, primarily of the Solar System, is one of the basic problems of celestial mechanics. The stability of motion of giant planets on cosmogonic time scales was established by numerical and analytical methods, but the question about the evolution of orbits of terrestrial planets and arbitrary solar-type planetary systems remained open. This work initiates a series of papers allowing one to advance in solving the problem of the evolution of the solar-type planetary systems on cosmogonic time scales by using powerful analytical tools. In the first paper of this series, we choose the optimum reference system and obtain the Poisson series expansion of the Hamiltonian of the problem in all Keplerian elements. We propose to use the integral representation of the corresponding coefficients or the Poisson processor means instead of conventionally addressing any possible special functions. This approach extremely simplifies the algorithm. The next paper of this series deals with the calculation of the expansion coefficients.",
author = "K. Kholshevnikov and Greb, {Alexandr V.} and Kuznetsov, {E. d.}",
year = "2001",
doi = "10.1023/A:1010487107989",
language = "English",
volume = "35",
pages = "243--248",
journal = "Solar System Research",
issn = "0038-0946",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "3",

}

RIS

TY - JOUR

T1 - The Expansion of the Hamiltonian of the Planetary Problem into the Poisson Series in All Keplerian Elements (Theory)

AU - Kholshevnikov, K.

AU - Greb, Alexandr V.

AU - Kuznetsov, E. d.

PY - 2001

Y1 - 2001

N2 - The study of the evolution of planetary systems, primarily of the Solar System, is one of the basic problems of celestial mechanics. The stability of motion of giant planets on cosmogonic time scales was established by numerical and analytical methods, but the question about the evolution of orbits of terrestrial planets and arbitrary solar-type planetary systems remained open. This work initiates a series of papers allowing one to advance in solving the problem of the evolution of the solar-type planetary systems on cosmogonic time scales by using powerful analytical tools. In the first paper of this series, we choose the optimum reference system and obtain the Poisson series expansion of the Hamiltonian of the problem in all Keplerian elements. We propose to use the integral representation of the corresponding coefficients or the Poisson processor means instead of conventionally addressing any possible special functions. This approach extremely simplifies the algorithm. The next paper of this series deals with the calculation of the expansion coefficients.

AB - The study of the evolution of planetary systems, primarily of the Solar System, is one of the basic problems of celestial mechanics. The stability of motion of giant planets on cosmogonic time scales was established by numerical and analytical methods, but the question about the evolution of orbits of terrestrial planets and arbitrary solar-type planetary systems remained open. This work initiates a series of papers allowing one to advance in solving the problem of the evolution of the solar-type planetary systems on cosmogonic time scales by using powerful analytical tools. In the first paper of this series, we choose the optimum reference system and obtain the Poisson series expansion of the Hamiltonian of the problem in all Keplerian elements. We propose to use the integral representation of the corresponding coefficients or the Poisson processor means instead of conventionally addressing any possible special functions. This approach extremely simplifies the algorithm. The next paper of this series deals with the calculation of the expansion coefficients.

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U2 - 10.1023/A:1010487107989

DO - 10.1023/A:1010487107989

M3 - Article

VL - 35

SP - 243

EP - 248

JO - Solar System Research

JF - Solar System Research

SN - 0038-0946

IS - 3

ER -

ID: 44109281