Relaxation oscillations in tidally evolving satellites

Celestial Mechanics and Dynamical Astronomy

Volumn 67, Issue 2, 1997, Pages 111-130

  Quinn, Dane ^a   Gladman, Brett ^b   Nicholson, Phil ^b   Rand, Richard ^b  

^a The University of Akron   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

Cassini states; Limit cycles; Relaxation oscillations; Singular perturbations; Tidal despinning

Indexed keywords

EID: 0040523194     PISSN: 09232958     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008240717133     Document Type: Article

References (14)

1. Beletskii, V. V.: 1972, Resonance rotation of celestial bodies and Cassini's laws. Celestial Mechanics 6, 356-378.
2. Bender, Carl W. and Orszag, Steven A.: 1978, Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill, Inc., New York.
3. Doedel, Eusebius: 1986, AUTO: Software for continuation and bifurcation problems in ordinary differential equations. Applied mathematics reports, California Institute of Technology.
4. Eckhaus, Wiktor: 1983, Relaxation oscillations including a standard chase on french ducks. In: Lecture Notes in Mathematics 985, Asymptotic Analysis II-Surveys and New Trends, Springer-Verlag, New York, pp. 449-494.
5. Gladman, Brett J., Quinn, D. Dane, Nicholson, Phil and Rand, Richard H.: 1996, Synchronous locking of tidally evolving satellites. Icarus 122, 166-192.
6. Guckenheimer, John and Holmes, Phillip J.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences 42. Springer-Verlag, New York.
7. Hale, Jack K. and Koçak, Hüseyin: 1991, Dynamics and Bifurcations. Springer-Verlag, New York.
8. Henrard, Jacques and Murigande, Charles: 1987, Colombo's top. Celestial Mechanics 40, 345-366.
9. Holden, Lisa and Erneux, Thomas: 1993, Slow passage through a Hopf bifurcation: From oscillatory to steady state solutions. SIAM Journal on Applied Mathematics 53(4), 1045-1058.
10. Holden, Lisa and Erneux, Thomas: 1993, Understanding bursting oscillations as periodic slow passages through bifurcation and limit points. Journal of Mathematical Biology 31, 351-365.
11. Lichtenberg, Allen J. and Lieberman, Michael A.: 1992, Regular and Chaotic Dynamics. Applied Mathematical Sciences 38. 2nd ed. Springer-Verlag, New York.
12. Peale, Stanton J.: 1969, Generalized Cassini's laws. Astronomical Journal 74, 483-489.
13. Peale, Stanton J.: 1974, Possible histories of the obliquity of Mercury. Astronomical Journal 79, 722-744.
14. Ward, William R.: 1975, Past orientation of the lunar spin axis. Science 189, 377-379.