Abstract
This paper continues the mathematical study of spin/orbit coupling which was begun in earlier articles by the second author. The equation studied is\(\ddot \theta = \varepsilon P(t,\theta ) + \varepsilon T(t,\dot \theta )\) whereP andT are periodic int and the angle θ. No specific form forP andT is assumed but only the conditions necessary to analyze the system near resonance or a ground state. The behavior of an averaged system of these equations is shown to be reflected qualitatively in the actual equations by rigorous mathematical methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Burns, T. J.: 1979,Celes. Mech. 19, 297.
Counselman, C. C. and Shapiro, I. I.: 1970,Symp. Math. 3, 121.
Goldreich, P. and Peale, S.: 1966,Astron. J. 71, 425.
Hale, J.: 1969,Ordinary Differential Equations, Wiley-Interscience, New York.
Kyner, W. T.: 1970, ‘Passage Through Resonance’, in G. E. O. Giacaglia (ed.),Periodic Orbits, Stability, and Resonances, D. Reidel Publ. Co., Dordrecht, Holland, 501.
Murdock, J.: 1975,J. Diff. Eq. 17, 361.
Murdock, J.: 1978,Celes. Mech. 18, 237.
Murdock, J. and Robinson, C.: 1980,J. Diff. Eq. 36, 425.
Newhouse, S. and Palis, J.: 1973, ‘Bifurcation of Morse-Smale Dynamical Systems’, in M. M. Peixoto (ed.),Dynamical Systems, Academic Press, New York, 303.
Robinson, C.: 1980,J. Diff. Eq. 37, 1.
Siegel, L. and Moser, J.: 1971,Lectures on Celestial Mechanics, Springer-Verlag, New York.
Author information
Authors and Affiliations
Additional information
This research was partially supported by NSF Grant MCS 79-01080.
Rights and permissions
About this article
Cite this article
Robinson, C., Murdock, J. Some mathematical aspects of spin-orbit resonance. II. Celestial Mechanics 24, 83–107 (1981). https://doi.org/10.1007/BF01228795
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01228795