Semi-analytical methods in orbital dynamics: leveraging computational advances for improved dynamical analysis
- Paper ID
96466
- DOI
- author
- company
Northwestern Polytechnical University; Universitat Politecnica de Catalunya (UPC); Northwestern Polytechnical University;National Key Laboratory of Aerospace Flight Dynamics; National Key Laboratory of Aerospace Flight Dynamics,Northwestern Polytechnical University,Xi'an
- country
China
- year
2025
- abstract
Advancements in computer technology and computational power have revolutionized problem-solving across various scientific and engineering fields, particularly in astrodynamics and orbital dynamics. Problems that were once intractable due to their complexity can now be tackled using semi-analytical approaches, which blend numerical simulations with analytical methods. These improvements not only enable more precise modeling and faster computations, making previously unaffordable challenges more manageable, but most importantly, they provide a deeper understanding of the underlying dynamics. Classical techniques such as Floquet transformations, Taylor and Fourier-Taylor expansions are now incorporated into modern semi-analytical methods like Jet Transport, parameterization techniques, and normal-form expansions. These tools enable a more comprehensive analysis, not only for the vicinity of equilibrium points but also of the neighborhoods of periodic orbits, providing deeper insights into both autonomous and non-autonomous dynamical models. This enhanced understanding leads to improved predictions, optimization, and station-keeping control, while also extending analysis capabilities toward quasi-periodic solutions and unlocking new possibilities that were once beyond reach. The cislunar space is a key operational region for current and future spacecraft missions, including NASA’s planned Gateway station. To model motion in this environment, different dynamical frameworks are used. The CR3BP provides a basic representation, while the ER3BP incorporates the eccentricity of the Earth-Moon system. More complex models also consider the Sun’s influence, such as the BCP, though it has limitations, due to the incoherence of the motion of the primries and the lack of an accurate L2 equivalent. Alternative approaches, like the QBCP, aim to address these shortcomings by incorporating a more realistic representation of the Sun’s effect on the Earth and Moon. Most analyses in these dynamical models have traditionally focused on the properties of libration points and their vicinity, as they serve as key reference locations for mission design. The study of the surrounding regions of periodic and quasi-periodic orbits has often been limited to linearized dynamics, providing only very localized approximations of spacecraft motion. Given the variety of currently available models, as well as advancements in computational techniques and power, it's worthwhile to extend these investigations to gain a deeper understanding of larger neighborhoods in different regions. In this paper, we implement new Floquet procedures and semi-analytical techniques to study different families of periodic and quasi-periodic orbits in different models. In particular, we analyze the neighborhood of the resonant 2:1 halo orbit, as well as the 3:1 and 9:2 NRHO, in the cislunar Earth-Moon system.