Abstract
It is shown that the characteristic exponents can be exactly expressed for a type of second order linear ordinary differential equations with periodic coefficients (Hill's equation) which appear as the variational equations of certain periodic solutions of dynamical systems. Key points are the transformation of the equation to the Gauss' hypergeometric differential equation, and evaluation of the trace of monodormy matrix in the complex plane of the independent variable. Two simple examples are given for which the stability of periodic solutions is rigorously analyzed.
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References
Contopoulos, G. and Zikides, M.: 1980,Astron. Astrophys. 90, 198.
Heggie, D. C.: 1983,Celest. Mech. 29, 207.
Plemelj, J.: 1962,Problems in the Sense of Riemann and Klein, Interscience Publishers, New York.
Poincaré, H.: 1892,Les méthodes nouvelles de la mécanique céleste, Vol. 1.
Whittaker, E. T.: 1936,A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press, New York.
Whittaker, E. T. and Watson, G. N.: 1962,A Course of Modern Analysis, Cambridge University Press, New York.
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Yoshida, H. A type of second order linear ordinary differential equations with periodic coefficients for which the characteristic exponents have exact expressions. Celestial Mechanics 32, 73–86 (1984). https://doi.org/10.1007/BF01358404
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DOI: https://doi.org/10.1007/BF01358404