Differential algebra methods applied to continuous abacus generation and bifurcation detection: application to periodic families of the Earth–Moon system

The return of human space missions to the Moon puts Earth–Moon system (EMS) at center attention. Hence, studying periodic solutions circular restricted three-body problem (CR3BP) is crucial ease transfer computations, find new solutions, or better understand these orbits. This work proposes a novel continuation method families using differential algebra (DA) mapping. We exploit DA with automatic control truncation error represent each family orbits as set 2D Taylor polynomial maps. These maps guarantee access any point without numerical propagation, providing continuous abacus. When applied halo $$L_1$$ and $$L_2$$ , planar Lyapunov distant retrograde orbit (DRO) family, butterfly we show that DA-based mapping asymptotically more efficient than point-wise methods by least two orders magnitude, controlled accuracy. To assist computation orbits, propose bifurcation detection algorithm enables family’s criteria. A study on shows identical results while highlighting undocumented bifurcations.