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K.V. Kholshevnikov (1973)
Astronomiya i geodeziya
M. Efroimsky, A. Escapa (2005)
The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variablesCelestial Mechanics and Dynamical Astronomy, 98
H. Kinoshita (1972)
First-order perturbations of the two finite body problemPublications of the Astronomical Society of Japan, 24
(1985)
Asimptoticheskie metody nebesnoi mekhaniki
A. Deprit, A. Elipe (1993)
Complete Reduction of the Euler-Poinsot ProblemJ. Astronaut. Sci., 41
(1983)
Spacecraft Dynamics
J. Getino, J. Ferrándiz (1990)
A Hamiltonian theory for an elastic earth: Canonical variables and kinetic energyCelestial Mechanics and Dynamical Astronomy, 49
J. Navarro, J. Ferrándiz (2002)
A New Symbolic Processor for the Earth Rotation TheoryCelestial Mechanics and Dynamical Astronomy, 82
K. Abdullah, A. Albouy (2005)
On a strange resonance noticed by M. Herman
H. Poincaré (1897)
Sur une forme nouvelle des équations du problème des trois corpsActa Mathematica, 21
H. Yoshida (1993)
Recent progress in the theory and application of symplectic integratorsCelestial Mechanics and Dynamical Astronomy, 56
H. Kinoshita, J. Souchay (1990)
The theory of the nutation for the rigid earth model at the second orderCelestial Mechanics and Dynamical Astronomy, 48
nirvikar Saran (1931)
Text-Book on Spherical AstronomyNature, 128
H. Poincaré (1897)
Sur une forme nouvelle des équations du problème des trois corpsBulletin Astronomique, 14
L. Petrov (2006)
The empirical Earth rotation model from VLBI observationsAstronomy and Astrophysics, 467
M. Moons (1982)
Physical Libration of the MoonCelestial Mech., 26
M. Moutsoulas (1970)
The physical libration of the moon.Earth Moon and Planets
(1866)
Mémoire sur l'emploi de la méthode de la variation des arbitraires dans théorie des mouvements de rotations
T. Fukushima, H. Ishizaki (1994)
Elements of spin motionCelestial Mechanics and Dynamical Astronomy, 59
M. Efroimsky (2005)
Gauge Freedom in Orbital MechanicsAnnals of the New York Academy of Sciences, 1065
A. Deprit (1967)
Free Rotation of a Rigid Body Studied in the Phase PlaneAmerican Journal of Physics, 35
Annales de l'Ecole Normale Supérieure, 1 re série, 1869
R. Radau
Sur la rotation des corps solidesAnnales Scientifiques De L Ecole Normale Superieure, 6
B. Murray, W. Ward, Sze Yeung (1973)
Periodic Insolation Variations on MarsScience, 180
M. Moutsoulas (1968)
Theory of orbitsAstrophysics and Space Science, 1
J. Marsden, T. Ratiu (1999)
Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems
F. Tisserand
Traité de mécanique céleste, 7
M. Efroimsky (2004)
On the theory of canonical perturbations and its application to Earth rotationarXiv: Astrophysics
A. Deprit (1969)
Canonical transformations depending on a small parameterCelestial mechanics, 1
W. Ward (1973)
Large-Scale Variations in the Obliquity of MarsScience, 181
G. Giacaglia, W. Jefferys (1971)
Motion of a space station. ICelestial mechanics, 4
J. Henrard (2005)
The rotation of IoIcarus, 178
K. Schreiber, A. Velikoseltsev, Markus Rothacher, T. Klügel, G. Stedman, D. Wiltshire (2004)
Direct measurement of diurnal polar motion by ring laser gyroscopesJournal of Geophysical Research, 109
W. Newman, M. Efroimsky (2003)
The method of variation of constants and multiple time scales in orbital mechanics.Chaos, 13 2
C. Leubner (1981)
Correcting a widespread error concerning the angular velocity of a rotating rigid bodyAmerican Journal of Physics, 49
P. Goldreich (1965)
Inclination of satellite orbits about an oblate precessing planetThe Astronomical Journal, 70
H. Plummer (1919)
An Introductory Treatise on Dynamical Astronomy
A. Bloch, P. Gurfil, K. Lum (2007)
The Serret-Andoyer formalism in rigid-body dynamics: II. Geometry, stabilization, and controlRegular and Chaotic Dynamics, 12
K. Lum, A. Bloch (1999)
Generalized Serret-Andoyer Transformation and Applications for the Controlled Rigid BodyDynamics and Control, 9
M. Efroimsky (2002)
Equations for the orbital elements: Hidden Symmetry
M. Efroimsky (2004)
Long-Term Evolution of Orbits About A Precessing Oblate Planet: 1. The Case of Uniform PrecessionCelestial Mechanics and Dynamical Astronomy, 91
V. Brumberg, L. Evdokimova, N. Kochina (1971)
Analytical methods for the orbits of artificial satellites of the MoonCelestial mechanics, 3
K. Kholshevnikov (1973)
Lie transformations in celestial mechanics.
J. Marsden, T. Ratiu (1994)
Introduction to mechanics and symmetry
H. Andoyer
Cours de mécanique céleste
H. Kinoshita, K. Nakajima, Y. Kubo, I. Nakagawa, Tsutomu Sasao, K. Yokoyama (1979)
Note on nutation in ephemerides.
D. Boccaletti, G. Pucacco (2004)
Theory of orbits : Volume 2 : Perturbative and geometrical methods
C. Jacobi, A. Clebsch
Vorlesungen über dynamik
P. Bretagnon, P. Rocher, J. Simon (1997)
Theory of the rotation of the rigid EarthAstronomy and Astrophysics, 319
G. Hori (1966)
Theory of general perturbations with unspecified canonical variablesPublications of the Astronomical Society of Japan, 18
W. Ward (1974)
Climatic variations on Mars: 1. Astronomical theory of insolationJournal of Geophysical Research, 79
A. Escapa, J. Getino, J. Ferrándiz (2002)
Indirect effect of the triaxiality in the Hamiltonian theory for the rigid earth nutationsAstronomy and Astrophysics, 389
(1850)
Eine neue Loesung des Problems der Rotation
(2009)
Submitted to ”Astronomy and Astrophysics” Implicit gauge symmetry emerging in the N-body problem of celestial mechanics.
H. Kinoshita (1977)
Theory of the Rotation of the Rigid EarthCelestial Mech., 15
M. Efroimsky, P. Goldreich (2004)
Submitted to ” Astronomy and Astrophysics ” Gauge Freedom in the N-body problem of Celestial Mechanics
J. Touma, J. Wisdom (1993)
The Chaotic Obliquity of MarsScience, 259
H. Schaub, J. Junkins (2003)
Analytical Mechanics of Space Systems
M. Efroimsky, P. Goldreich (2004)
Gauge Freedom in the N-Body Problem of Celestial MechanicsAstronomy & Astrophysics, 415
(1866)
VorlesungenVorlesungen¨Vorlesungenüber Dynamik. G. Reimer
J. Touma, J. Wisdom (1994)
Lie-Poisson integrators for rigid body dynamics in the solar systemThe Astronomical Journal, 107
J. Getino, J. Ferrándiz (1991)
A Hamiltonian theory for an elastic earth: First order analytical integrationCelestial Mechanics and Dynamical Astronomy, 51
I. Sadov (1970)
The action-angle variables in the Euler-Poinsot problem: PMM vol. 34, n≗5, 1970, pp. 962–964Journal of Applied Mathematics and Mechanics, 34
A. Escapa, J. Getino, J. Ferrándiz (2001)
Canonical approach to the free nutations of a three‐layer Earth modelJournal of Geophysical Research, 106
V. Brumberg (1991)
Essential Relativistic Celestial Mechanics
M. Efroimsky, P. Goldreich (2003)
Gauge symmetry of the N-body problem in the Hamilton–Jacobi approachJournal of Mathematical Physics, 44
J. Laskar, P. Robutel (1993)
The chaotic obliquity of the planetsNature, 361
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.
Regular and Chaotic Dynamics – Springer Journals
Published: Aug 11, 2007
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