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Article analysis:

This article provides an overview of the transfer of differential algebra (DA)-based normal form methods from particle beam physics and accelerator physics to astrodynamics for designing bounded motion in the Earth’s zonal problem. The article is well-structured and clearly written, providing a comprehensive overview of both analytic and numerical approaches that have been used previously for this purpose. It also presents a new approach using DA-based normal form (DANF) methods, which it claims can overcome limitations of previous approaches by enabling calculation of entire sets of bounded orbits extending up to thousands of kilometers with a stable relative motion for decades in the full zonal problem.

The article appears to be reliable overall, as it provides detailed information on both existing approaches and its own proposed approach, as well as examples demonstrating its effectiveness. However, there are some potential biases that should be noted. For example, while the article does mention existing analytical approaches such as those by Schaub and Alfriend (2001), Gim and Alfriend (2003), Schweighart and Sedwick (2002), Gurfil (2007), Dang et al. (2015), Chu et al. (2015), Martinusi and Gurfil (2011) etc., it does not provide any critical analysis or comparison between them or their respective strengths/weaknesses compared to its own proposed approach using DANF methods. Additionally, while it mentions numerical approaches such as those by Broucke (1994), Koon et al. (2001) etc., it does not provide any details on how they compare with its own proposed approach either in terms of accuracy or computational time/complexity etc., which could be useful for readers who are considering using either approach for their own applications