Differential algebra mappings of CR3BP periodic solutions

This dataset is made of twenty-three items containing polynomial mappings of families of periodic solutions of the circular restricted 3-body problem (CR3BP) [1], here the Earth-Moon and the Sun-(Earth-Moon) systems. Each file stores a list of differential algebra (DA) [2] maps representing these families with their associated domains of definition. The DA maps were computed using DA solving of two-point boundary value problem [3] and allow one to access initial conditions of solutions of the CR3BP by polynomial evaluation instead of heavy computations, provided the files containing the DA polynomials [4]. Each family is available with three different accuracies, also called tolerances. They are, with increasing accuracy, 1e-5, 1e-8, and 1e-10. The most accurate ones have higher loading and evaluation times and use more disk space but give better approximations of the families. The code DAHALOa_reader allows to read these files and can on GitHub: ThomasClb/DAHALOa_reader (github.com) <strong>References</strong><br> [1] V. Szebehely, ‘Theory of Orbit', Academic Press, 1967, pp. 7-41. DOI: 10.1016/B978-0-12-395732-0.50007-6<br> [2] R. Armellin, P. Di Lizia, et al., ’Asteroid close encounters characterization using differential algebra: the case of Apophis', Celestial Mechanics and Dynamical Astronomy, Vol. 107, No. 4, 2010, pp. 451-470. DOI: 10.1007/s10569-010-9283-5<br> [3] P. Di Lizia, R. Armellin, and M. Lavagna, 'Application of high order expansions of two-point boundary value problems to astrodynamics', Celestial Mechanics and Dynamical Astronomy, Vol. 102, No. 4, 2008, pp. 355-375. DOI: 10.1007/s10569-008-9170-5<br> [4] T. Caleb, M. Losacco, A. Fossà, R. Armellin, and S. Lizy-Destrez, 'Differential algebra methods applied to continuous abacus generation and bifurcation detection: application to periodic families of the Earth–Moon system', Nonlinear dynamics, Vol. 111, 2023, pp. 9721-9740. DOI: 10.1007/s11071-023-08375-0