Motion of a space station. I

Giacáglia, Giorgio Eugenio Oscare; Jefferys, W. H.

doi:10.1007/bf01231403

Cited by 19 publications

(9 citation statements)

References 2 publications

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“…Interestingly, the climate is much more sensitive to the obliquity of the planet than to the eccentricity of its orbit. (Murray et al [47], Ward [48], [49]) The canonical theory of rotation of a rigid body in a precessing coordinate frame was pioneered by Giacaglia and Jefferys [31]. It was based on the Andoyer variables and was used by the authors to describe rotation of a space station.…”

Section: Physical Motivationmentioning

confidence: 99%

The Serret-Andoyer formalism in rigid-body dynamics: I. Symmetries and perturbations

et al. 2007

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This paper reviews the Serret-Andoyer (SA) canonical formalism in rigid-body dynamics, and presents some new results. As is well known, the problem of unsupported and unperturbed rigid rotator can be reduced. The availability of this reduction is offered by the underlying symmetry, that stems from conservation of the angular momentum and rotational kinetic energy. When a perturbation is turned on, these quantities are no longer preserved. Nonetheless, the language of reduced description remains extremely instrumental even in the perturbed case. We describe the canonical reduction performed by the Serret-Andoyer (SA) method, and discuss its applications to attitude dynamics and to the theory of planetary rotation. Specifically, we consider the case of angular-velocity-dependent torques, and discuss the variation-of-parameters-inherent antinomy between canonicity and osculation. Finally, we address the transformation of the Andoyer variables into action-angle ones, using the method of Sadov.

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Section: Physical Motivationmentioning

confidence: 99%

The Serret-Andoyer formalism in rigid-body dynamics: I. Symmetries and perturbations

et al. 2007

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“…For arbitrary gravitational bodies and for artificial satellites, it is sometimes preferable to use Cartesian coordinates and inertia coefficients. Giacaglia and Jefferys (1971) formulated computer algebra for evaluating the series expansion of spherical harmonics in terms of Delaunay variables. The potential is expanded up to the second-order (with equivalence to MacCullagh's formula).…”

Section: Introductionmentioning

confidence: 99%

Mutual gravitational potential and torque of solid bodies via inertia integrals

Ashenberg

2007

Celestial Mech Dyn Astr

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The mutual gravitational potential and the mutual gravitational torque of two bodies of arbitrary shape are expanded to the fourth order. The derivations are based on Cartesian coordinates, inertia integrals with relation to the principal reference frames of each body, and the relative rotation matrix. The current formulation is convenient to utilize in high precision problems in rotational dynamics.

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“…The Andoyer variables are often chosen as rotational elements (Andoyer 1923, Giacaglia & Jefferys 1971, Kinoshita 1972, though other sets of canonical elements have appeared in the literature (Richelot 1850;Serret 1866;Peale 1973Peale , 1976Deprit & Elipe 1993;Fukushima & Ishizaki 1994) 1 . After a transition to rotational elements is performed within the undisturbed Euler-Poinsot setting, the next step is to extend this method to a forced-rotation case.…”

Section: Historical Preliminariesmentioning

confidence: 99%

“…expression equivalent to formulae (24 -25) in Giacaglia & Jefferys (1971). 20 Now let us employ the machinery set out in subsection 2.2.…”

Section: The Andoyer Variables Introduced In a Precessing Frame A 11mentioning

confidence: 99%

The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables

Efroimsky

Escapa

2007

Celestial Mech Dyn Astr

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In the method of variation of parameters we express the Cartesian coordinates or the Euler angles as functions of the time and six constants. If, under disturbance, we endow the "constants" with time dependence, the perturbed orbital or angular velocity will consist of a partial time derivative and a convective term that includes time derivatives of the "constants". The Lagrange constraint, often imposed for convenience, nullifies the convective term and thereby guarantees that the functional dependence of the velocity on the time and "constants" stays unaltered under disturbance. "Constants" satisfying this constraint are called osculating elements. Otherwise, they are simply termed orbital or rotational elements. When the equations for the elements are required to be canonical, it is normally the Delaunay variables that are chosen to be the orbital elements, and it is the Andoyer variables that are typically chosen to play the role of rotational elements. (Since some of the Andoyer elements are time-dependent even in the unperturbed setting, the role of "constants" is actually played by their initial values.) The Delaunay and Andoyer sets of variables share a subtle peculiarity: under certain circumstances the standard equations render the elements nonosculating.In the theory of orbits, the planetary equations yield nonosculating elements when perturbations depend on velocities. To keep the elements osculating, the equations must be amended with extra terms that are not parts of the disturbing function (Efroimsky & Goldreich

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Motion of a space station. I

Cited by 19 publications

References 2 publications

The Serret-Andoyer formalism in rigid-body dynamics: I. Symmetries and perturbations

The Serret-Andoyer formalism in rigid-body dynamics: I. Symmetries and perturbations

Mutual gravitational potential and torque of solid bodies via inertia integrals

The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables

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