Averaged Equations of Motion for a Perturbing Acceleration which Is Constant in Various Reference Frames

T.N. Sannikova, K.V. Kholshevnikov

Результат исследований: Научные публикации в периодических изданияхстатья

5 Цитирования (Scopus)

Выдержка

The motion of a zero-mass point under attraction to the central body and a disturbing acceleration $\mathbf P$ is considered. We suppose the vector $\mathbf P$ being constant in three mostly used in astronomy reference frames: the main inertial one $\mathcal O$, and two orbital ones $\mathcal O_k$ with $x$-axis directed along the radius-vector if $s=1$, and along the velocity vector if $s=2$. The ratio of $|\mathbf P|$ to the main acceleration due to the attraction to the central body is supposed to be small. Averaging transform is applied to the equations in osculating elements in the first order with respect to the small parameter. Closed expressions for the functions describing the change of variables as well as for the right-hand parts of equations in averaged elements are obtained. All functions appeared in the frames \mathcal O$, $\mathcal O_1$ are elementary; elliptical integrals emerge in the frame $\mathcal O_2$. All quantities we need are developed in series in powers of the eccentricity $e$ converg
Язык оригиналаанглийский
Страницы (с-по)945-953
ЖурналAstronomy Reports
Том58
Номер выпуска12
DOI
СостояниеОпубликовано - 2014

Отпечаток

equations of motion
attraction
astronomy
eccentricity
transform
orbitals
radii
need
parameter

Цитировать

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Averaged Equations of Motion for a Perturbing Acceleration which Is Constant in Various Reference Frames. / Sannikova, T.N.; Kholshevnikov, K.V.

В: Astronomy Reports, Том 58, № 12, 2014, стр. 945-953.

Результат исследований: Научные публикации в периодических изданияхстатья

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AU - Sannikova, T.N.

AU - Kholshevnikov, K.V.

PY - 2014

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N2 - The motion of a zero-mass point under attraction to the central body and a disturbing acceleration $\mathbf P$ is considered. We suppose the vector $\mathbf P$ being constant in three mostly used in astronomy reference frames: the main inertial one $\mathcal O$, and two orbital ones $\mathcal O_k$ with $x$-axis directed along the radius-vector if $s=1$, and along the velocity vector if $s=2$. The ratio of $|\mathbf P|$ to the main acceleration due to the attraction to the central body is supposed to be small. Averaging transform is applied to the equations in osculating elements in the first order with respect to the small parameter. Closed expressions for the functions describing the change of variables as well as for the right-hand parts of equations in averaged elements are obtained. All functions appeared in the frames \mathcal O$, $\mathcal O_1$ are elementary; elliptical integrals emerge in the frame $\mathcal O_2$. All quantities we need are developed in series in powers of the eccentricity $e$ converg

AB - The motion of a zero-mass point under attraction to the central body and a disturbing acceleration $\mathbf P$ is considered. We suppose the vector $\mathbf P$ being constant in three mostly used in astronomy reference frames: the main inertial one $\mathcal O$, and two orbital ones $\mathcal O_k$ with $x$-axis directed along the radius-vector if $s=1$, and along the velocity vector if $s=2$. The ratio of $|\mathbf P|$ to the main acceleration due to the attraction to the central body is supposed to be small. Averaging transform is applied to the equations in osculating elements in the first order with respect to the small parameter. Closed expressions for the functions describing the change of variables as well as for the right-hand parts of equations in averaged elements are obtained. All functions appeared in the frames \mathcal O$, $\mathcal O_1$ are elementary; elliptical integrals emerge in the frame $\mathcal O_2$. All quantities we need are developed in series in powers of the eccentricity $e$ converg

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KW - disturbing acceleration

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DO - 10.1134/S1063772914120099

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