Abstract
We analyse in details a simple dynamical system proposed by G. Colombo for the description of the rotational state of planets and satellites. We show that the derivatives of the critical areas are simple analytical functions of the parameters of the problem. These quantities are instrumental in computing the probabilities of capture of the precession of the spin axis in resonance with the precession of the orbit.
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References
Beletskii, V.V., 1972, Resonance Rotation of Celestial Bodies and Cassini's Laws. Celest. Mech. 356–378.
Borderies, N., 1980, La rotation de Mars. Thesis. Univ. Paul Sabatier, Toulouse, France.
Bretagnon, P., 1974, Termes à lengues périodes dans le Système Solaire. Astron. Astrophys. 30, 141–162.
Cassini, G.D., 1963, Traité de l'Origine et des Progrès de l'Astronomie (Paris).
Colombo, G., 1966, Cassini's Second and Third Laws. Astron. J. 71, 891–896.
Deprit, A., 1967, Free Rotation of a Rigid Body Studies in the Phase Plane. Am. J. of Physics, 35, 424–428.
Cary, J.R., Escande, D.F. and Tennyson, J.L., 1987, Adiabatic Invariant change due to Separatrix Crossing. Phys. Rev. A, 34, 4256–4257.
Escande, D.F., 1985, Changes of Adiabatic Invariant at Separatrix Crossing: Application to Slow Hamiltonian Chaos, in: “Advances in nonlinear dynamics and stochastic process (R. Livi and A. Politi eds) World Scientific, Singapore, pp. 67–79.
Henrard, J., 1982, Capture into resonance: An extension of the use of Adiabatic Invariants. Celest. Mech. 27, 3–22.
Henrard, J., 1987, The Adiabatic Invariant in Classical Mechanics, submitted for publication in Dynamics reported.
Henrard, J. and Lemaître, A., 1983, A Second Fundamental Model for Resonance, Celest. Mech. 30, 197–218.
Henrard, J. and Moons, M., 1978, Hamiltonian Theory of the Libration of the Moon. Dynamics of Planets and Satellites (V. Szebehely ed.) Reidel P.C.
Kinoshita, H., 1975, Formulas for Precession. Smithsonian Astrophys. Obs. Special Report, no364.
Kinoshita, H., 1977, Theory of the Rotation of the Rigid Earth. Celest. Mech. 15, 277–326.
Moons, M., 1982, Physical Libration of the Moon, Celest. Mech. 26, 131–142.
Moons, M., 1984, Planetary Perturbations on the Libration of the Moon, Celest. Mech. 34, 263–273.
Peale, S.J., 1969, Generalized Cassini's Laws, Astron. J. 74, 483–489.
Peale, S.J., 1974, Possible Histories of the Obliquity of Mercury, Astron. J. 79, 722–744.
Squyres, S.W., 1984, The History of Water on Mars, Ann. Rev. Earth Planet. Sci. 12, 83–106.
Ward, W.R., 1975, Tidal Friction and Generalized Cassini's Laws in the Solar System, Astron. J. 80, 64–70.
Ward, W.R., Burns, J.A., and Toon, O.B., 1979, Past Obliquity Oscillations of Mars: The Role of the Tharsis Uplift, J. of Geophy. R. 84, 243–258.
Yoder, C.F., 1979, Diagrammatic Theory of Transition of Pendulum Like Systems, Celest. Mech. 19, 3–30.
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dedicated to the memory of G. Colombo.
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Henrard, J., Murigande, C. Colombo's top. Celestial Mechanics 40, 345–366 (1987). https://doi.org/10.1007/BF01235852
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DOI: https://doi.org/10.1007/BF01235852