Journal of Fixed Point Theory and Applications

, Volume 5, Issue 2, pp 249–264

On the longitudinal librations of Hyperion

Article
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Abstract.

We study a nonlinear, second order ordinary differential equation that models the longitudinal librations of the longest axis L of a satellite with respect to the planet-satellite center line C. Combining theoretical arguments and numerical evidence we prove that, in the case of Hyperion, a satellite of Saturn, the angle A between L and C can change in a chaotic manner at the moments when the distance from Hyperion to Saturn reaches its minimum value. More precisely, given an arbitrary sequence of zeros and ones, we show that there is at least one initial velocity of A such that its successive positions reproduce the given sequence.

Mathematics Subject Classification (2000).

34K23 34C25 

Keywords.

Longitudinal librations equivariance symbolic dynamics chaotic behavior 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Massimo Furi
    • 1
  • Adam S. Landsberg
    • 2
  • Mario Martelli
    • 3
  1. 1.Dipartimento di Matematica Applicata “Giovanni Sansone”Università degli Studi di FirenzeFirenzeItaly
  2. 2.Joint Science DepartmentClaremont McKenna, Pitzer, and Scripps CollegesClaremontUSA
  3. 3.Department of MathematicsClaremont Graduate UniversityClaremontUSA

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