Expansion of the Hamiltonian for the planetary problem into a Poisson series in the heliocentric reference frame

Research output

1 Citation (Scopus)

Abstract

An expansion of the Hamiltonian for the N-planet problem into a Poisson series using a system of modified (complex) Poincare´ canonical elements in the heliocentric coordinate system is constructed. The Lagrangian and Hamiltonian formalisms are used. The first terms in the expansions of the principal and complementary parts of the disturbing function are presented. Estimates of the number of terms in the presented expansions have been obtained through numerical experiments. A comparison with the results of other authors is made.

Original languageRussian
Pages (from-to)555-566
Number of pages12
JournalAstronomy Letters
Volume42
Issue number8
DOIs
Publication statusPublished - 1 Aug 2016

Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

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title = "Expansion of the Hamiltonian for the planetary problem into a Poisson series in the heliocentric reference frame",
abstract = "An expansion of the Hamiltonian for the N-planet problem into a Poisson series using a system of modified (complex) Poincare´ canonical elements in the heliocentric coordinate system is constructed. The Lagrangian and Hamiltonian formalisms are used. The first terms in the expansions of the principal and complementary parts of the disturbing function are presented. Estimates of the number of terms in the presented expansions have been obtained through numerical experiments. A comparison with the results of other authors is made.",
keywords = "disturbing function, Hamiltonian, heliocentric coordinates, Laplace coefficients, N-body problem, Poincar{\'e} canonical elements, Poisson series",
author = "Mikryukov, {D. V.}",
year = "2016",
month = "8",
day = "1",
doi = "10.1134/S106377371608003X",
language = "русский",
volume = "42",
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issn = "1063-7737",
publisher = "МАИК {"}Наука/Интерпериодика{"}",
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AU - Mikryukov, D. V.

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N2 - An expansion of the Hamiltonian for the N-planet problem into a Poisson series using a system of modified (complex) Poincare´ canonical elements in the heliocentric coordinate system is constructed. The Lagrangian and Hamiltonian formalisms are used. The first terms in the expansions of the principal and complementary parts of the disturbing function are presented. Estimates of the number of terms in the presented expansions have been obtained through numerical experiments. A comparison with the results of other authors is made.

AB - An expansion of the Hamiltonian for the N-planet problem into a Poisson series using a system of modified (complex) Poincare´ canonical elements in the heliocentric coordinate system is constructed. The Lagrangian and Hamiltonian formalisms are used. The first terms in the expansions of the principal and complementary parts of the disturbing function are presented. Estimates of the number of terms in the presented expansions have been obtained through numerical experiments. A comparison with the results of other authors is made.

KW - disturbing function

KW - Hamiltonian

KW - heliocentric coordinates

KW - Laplace coefficients

KW - N-body problem

KW - Poincaré canonical elements

KW - Poisson series

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U2 - 10.1134/S106377371608003X

DO - 10.1134/S106377371608003X

M3 - статья

AN - SCOPUS:84981713474

VL - 42

SP - 555

EP - 566

JO - Astronomy Letters

JF - Astronomy Letters

SN - 1063-7737

IS - 8

ER -