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The Conservation of Area Integrals in Averaging Transformations. / Kuznetsov, E. D.
In: Astronomy Reports, Vol. 54, No. 6, 01.06.2010, p. 562-569.

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

Harvard

Kuznetsov, ED 2010, 'The Conservation of Area Integrals in Averaging Transformations', Astronomy Reports, vol. 54, no. 6, pp. 562-569. https://doi.org/10.1134/S1063772910060090

APA

Kuznetsov, E. D. (2010). The Conservation of Area Integrals in Averaging Transformations. Astronomy Reports, 54(6), 562-569. https://doi.org/10.1134/S1063772910060090

Vancouver

Kuznetsov ED. The Conservation of Area Integrals in Averaging Transformations. Astronomy Reports. 2010 Jun 1;54(6):562-569. doi: 10.1134/S1063772910060090

Author

Kuznetsov, E. D. / The Conservation of Area Integrals in Averaging Transformations. In: Astronomy Reports. 2010 ; Vol. 54, No. 6. pp. 562-569.

BibTeX

@article{c0c65b094a7143dcb736556fdc0fe0a2,
title = "The Conservation of Area Integrals in Averaging Transformations",
abstract = "It is shown for the two-planetary version of the weakly perturbed two-body problem that, in a system defined by a finite part of a Poisson expansion of the averaged Hamiltonian, only one of the three components of the area vector is conserved, corresponding to the longitudes measuring plane. The variability of the other two components is demonstrated in two ways. The first is based on calculating the Poisson bracket of the averaged Hamiltonian and the components of the area vector written in closed form. In the second, an echeloned Poisson series processor (EPSP) is used when calculating the Poisson bracket. The averaged Hamiltonian is taken with accuracy to second order in the small parameter of the problem, and the components of the area vector are expanded in a Poisson series.",
author = "Kuznetsov, {E. D.}",
year = "2010",
month = jun,
day = "1",
doi = "10.1134/S1063772910060090",
language = "English",
volume = "54",
pages = "562--569",
journal = "Astronomy Reports",
issn = "1063-7729",
publisher = "Pleiades Publishing",
number = "6",

}

RIS

TY - JOUR

T1 - The Conservation of Area Integrals in Averaging Transformations

AU - Kuznetsov, E. D.

PY - 2010/6/1

Y1 - 2010/6/1

N2 - It is shown for the two-planetary version of the weakly perturbed two-body problem that, in a system defined by a finite part of a Poisson expansion of the averaged Hamiltonian, only one of the three components of the area vector is conserved, corresponding to the longitudes measuring plane. The variability of the other two components is demonstrated in two ways. The first is based on calculating the Poisson bracket of the averaged Hamiltonian and the components of the area vector written in closed form. In the second, an echeloned Poisson series processor (EPSP) is used when calculating the Poisson bracket. The averaged Hamiltonian is taken with accuracy to second order in the small parameter of the problem, and the components of the area vector are expanded in a Poisson series.

AB - It is shown for the two-planetary version of the weakly perturbed two-body problem that, in a system defined by a finite part of a Poisson expansion of the averaged Hamiltonian, only one of the three components of the area vector is conserved, corresponding to the longitudes measuring plane. The variability of the other two components is demonstrated in two ways. The first is based on calculating the Poisson bracket of the averaged Hamiltonian and the components of the area vector written in closed form. In the second, an echeloned Poisson series processor (EPSP) is used when calculating the Poisson bracket. The averaged Hamiltonian is taken with accuracy to second order in the small parameter of the problem, and the components of the area vector are expanded in a Poisson series.

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U2 - 10.1134/S1063772910060090

DO - 10.1134/S1063772910060090

M3 - Article

VL - 54

SP - 562

EP - 569

JO - Astronomy Reports

JF - Astronomy Reports

SN - 1063-7729

IS - 6

ER -

ID: 37908905