Essays on the Motion of Celestial Bodies

Beletsky, V. V.; Lutze, FH

doi:10.1115/1.1623753

Cited by 41 publications

(58 citation statements)

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“…Использование переменных, аналогичных истинной аномалии, в задачах небес-ной механики начинается, вероятно, в публикациях [36,38]. Однако интенсивное применение ис-тинной аномалии в задачах динамики полета тесно связано с именем Белецкого [1][2][3] (см. также работы [17,19,22]).…”

Section: спутниковое приближение и истинная аномалия как независимая unclassified

“…Другая категория эффектов относится к возможности использования перераспределения масс КА для обеспечения поступатель-ного движения его центра масс. Эта идея, принадлежащая Белецкому и Гиверцу [2,4] и развитая Доновым [10], была предметом жарких дискуссий, в том числе и в научно-по-пулярной литературе [9]. Позднее аналогичные задачи интенсивно изучались [31,35,40], в частности, в рамках теории относительности [27,37,42].…”

Section: Introductionunclassified

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Motion of a satellite with a variable mass distribution in a central field of Newtonian attraction

Анатольевич¹,

Иванович²

2017

Nelin. Dinam.

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Section: спутниковое приближение и истинная аномалия как независимая unclassified

Section: Introductionunclassified

Motion of a satellite with a variable mass distribution in a central field of Newtonian attraction

Анатольевич¹,

Иванович²

2017

Nelin. Dinam.

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“…3a), i is inclination of the orbit. For a dynamically symmetrical body (A = B) when all perturbation forces are potential and independent on the angle of rotation ϕ, the system (11)-(16) becomes (Beletskii 1972;Beletsky 2001) …”

Section: Figmentioning

confidence: 99%

“…the rate of their change is of the order of a small parameter . For description of the rotational motion of a planet we used the variables (Beletsky 2001):…”

Section: Formulation and Basic Equationsmentioning

confidence: 99%

Rotational evolution of exoplanets under the action of gravitational and magnetic perturbations

Kitiashvili

Gusev

2008

Celestial Mech Dyn Astr

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We investigate the evolution of the rotational axes of exoplanets under the action of gravitational and magnetic perturbations. The planet is assumed to be dynamically symmetrical and to be magnetised along its dynamical-symmetry axis. By qualitative methods of the bifurcation theory of multiparametric PDEs, we have derived a gallery of 69 phase portraits. The portraits illustrate evolutionary trajectories of the angular momentum L of a planet for a variety of the initial conditions, for different values of the ratio between parameters describing gravitational and magnetic perturbations, and for different rates of the orbital evolution. We provide examples of the phase portraits, that reveal the differences in topology and the evolutionary track of L in the vicinity of an equilibrium state. We determine the bifurcation properties, i.e., the way of reorganisation of phase trajectories in the vicinities of equilibria; and we point out the combinations of parameters' values that permit ip-overs from a prograde to a retrograde spin mode.

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“…In this work we will adopt a realistic hypothesis called the Belestky hypothesis (Belestky 2001), which can be applied to diverse problems of celestial mechanics and astrodynamics. The Belestky hypothesis states that the distance from the spacecraft to the binary asteroid is much greater that the size of the spacecraft.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a triaxial gyrostat at a Lagrangian equilibrium of a binary asteroid

Vera

2009

Astrophys Space Sci

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The non-canonical Hamiltonian dynamics of a triaxial gyrostat in Newtonian interaction with two punctual masses is considered. This serves as a model for the study of the attitude dynamics of a spacecraft located at a Lagrangian equilibrium point of the system formed by a binary asteroid and a spacecraft. Using geometric-mechanics methods, the approximated dynamics that arises when developing the potential in series of Legendre functions and truncating the series to the second harmonics is studied. Working in the reduced problem, the existence of equilibria in Lagrangian form are studied, in analogy with classic results on the topic. In this way, the classical results on equilibria of the threebody problem, as well as other results by different authors that use more conventional techniques for the case of rigid bodies, are generalized. The rotational Poisson dynamics of a spacecraft located at a Lagrangian equilibrium and the study of the nonlinear stability of some important equilibria are considered. The analysis is done in vectorial form avoiding the use of canonical variables and the tedious expressions associated with them.

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Essays on the Motion of Celestial Bodies

Cited by 41 publications

References 0 publications

Motion of a satellite with a variable mass distribution in a central field of Newtonian attraction

Motion of a satellite with a variable mass distribution in a central field of Newtonian attraction

Rotational evolution of exoplanets under the action of gravitational and magnetic perturbations

Dynamics of a triaxial gyrostat at a Lagrangian equilibrium of a binary asteroid

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