Nonlinear Dynamics

, Volume 93, Issue 2, pp 453–462 | Cite as

Periodic motion around libration points in the Elliptic Restricted Three-Body Problem

  • Fabio Ferrari
  • Michèle Lavagna
Original Paper


Periodicity of motion around the collinear libration point associated with the Elliptic Restricted Three-Body Problem is studied. A survey of periodic solutions in the Circular Restricted Three-Body Problem is presented considering both Sun–Earth and Earth–Moon systems. Halo, Lyapunov and Vertical families around L1, L2 and L3 points are investigated, and their orbital period ranges through the entire family are reported. Resonant motions within the orbit families in the circular problem are identified and selected as suitable initial guess to find periodic orbits in the elliptic problem, which are targeted using a differential correction algorithm. Periodic solutions found are cataloged depending on the number of revolutions around libration points. Geometry, dynamical behavior and stability properties of single-revolution orbits are shown, as well as double-, triple- and quadruple-revolution solutions.


Periodic motion Three-Body Problem ER3BP 


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Aerospace Science and TechnologyPolitecnico di MilanoMilanItaly

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