Abstract
A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the long-term effects of gravity-gradient torque and orbital evolution on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is constrained to precess and spin with constant rates. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite to second order in n/ω0, where n is the orbital mean motion of the center of mass and ω0 is a reference value of the magnitude of the satellite’s rotational angular velocity. The differential equations derivable from the transformed Hamiltonian are integrable and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed and a comparison of theoretical results with observations is made.
This paper is a slightly modified version of a previously published paper (Cochran, 1972) by the author.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beletskii, V. V.: 1965, ‘Motion of an Artificial Satellite about Its Center of Mass’, NASA TT F-429.
Byrd, P. F. and Friedman, M. D.: 1954, Handbook of Elliptic Integrals for Engineers and Physicists, Springer-Verlag, Berlin.
Campbell, J. A. and Jefferys, W. H.: 1970, Celes. Mech 2, 467.
Cochran, J. E.: 1970, Dissertation, University of Texas, Austin.
Cochran, J. E.: 1972, Celes. Mech 6, 2, 213.
Colombo, G.: 1964, Acad. Press Appl. Math. 7, Academic Press, New York, 175.
Crenshaw, J. W. and Fitzpatrick, P. M.: 1968, AIAA J. 6, 2140.
Deprit, A.: 1967, Am. J. Phys 35, 424.
Fitzpatrick, P. M.: 1970, Principles Celes. Mech., Academic Press, New York, 348.
Henrad, J.: 1970, Celes. Mech 3, 107.
Hitzl, D. L. and Breakwell, J. V.: 1971, Celes. Mech 3, 346.
Holland, R. L.: 1969, Private communication.
Holland, R. L. and Sperling, H. J.: 1969, Astron. J 74, 490.
Hori, G.: 1966, Publ. Astron. Soc. Japan 18, 287.
LaPlace, P. S.: 1829, Mecanique Céleste, Vol. II, Chelsa Publishing Company, New York, Fifth Book, Chapters I-II.
MacMillan, W. D.: 1960, Dynamics of Rigid Bodies, Dover Publications, New York, Chapter V II.
Mersmann, W. A.: 1970, Celes. Mech 3, 81.
Tisserand, F.: 1891, Traité de Mécanique Céleste, Vol. II, Gauther-Villars, Paris, Chapters XXII-XXIII.
Whittaker, E. T.: 1965, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press, New York, 144.
Whittaker, E. T. and Watson, G.N.: 1927, Modern Analysis, Cambridge University Press, New York, 522.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1973 D. Reidel Publishing Company, Dordrecht-Holland
About this paper
Cite this paper
Cochran, J.E. (1973). Long-Term Motion in a Restricted Problem of Rotational Motion. In: Tapley, B.D., Szebehely, V. (eds) Recent Advances in Dynamical Astronomy. Astrophysics and Space Science Library, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2611-6_40
Download citation
DOI: https://doi.org/10.1007/978-94-010-2611-6_40
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-2613-0
Online ISBN: 978-94-010-2611-6
eBook Packages: Springer Book Archive