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A novel algorithm for generating libration point orbits about the collinear points

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Abstract

This paper presents a numerical algorithm that can generate long-term libration points orbits (LPOs) and the transfer orbits from the parking orbits to the LPOs in the circular-restricted three-body problem (CR3BP) and the full solar system model without initial guesses. The families of the quasi-periodic LPOs in the CR3BP can also be constructed with this algorithm. By using the dynamical behavior of LPO, the transfer orbit from the parking orbit to the LPO is generated using a bisection method. At the same time, a short segment of the target LPO connected with the transfer orbit is obtained, then the short segment of LPO is extended by correcting the state towards its adjacent point on the stable manifold of the target LPO with differential evolution algorithm. By implementing the correction strategy repeatedly, the LPOs can be extended to any length as needed. Moreover, combining with the continuation procedure, this algorithm can be used to generate the families of the quasi-periodic LPOs in the CR3BP.

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Acknowledgments

This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET:www.sharcnet.ca) and Compute/Calcul Canada.

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Authors and Affiliations

  1. Department of Earth and Space Science and Engineering, York University, Toronto, ON, M3J 1P3, Canada

    Yuan Ren & Jinjun Shan

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  1. Yuan Ren
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  2. Jinjun Shan
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Correspondence to Jinjun Shan.

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Ren, Y., Shan, J. A novel algorithm for generating libration point orbits about the collinear points. Celest Mech Dyn Astr 120, 57–75 (2014). https://doi.org/10.1007/s10569-014-9560-9

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