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Author: s | 2025-04-24

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Nonlinear Sci. 7(5), 427–473 (1997). ADS MathSciNet MATH Google Scholar Jorba-Cuscó, M., Farrés, A., Jorba, À.: Two periodic models for the Earth-Moon system. Front. Appl. Math. Stat. 4, 32 (2018). MATH Google Scholar Kelly, P., Junkins, J.L., Majji, M.: Resonant quasi-periodic orbits in the bi-elliptic restricted four-body problem. In: AAS/AIAA Astrodynamics Specialist Conference, Big Sky, Montana, August 13-17, 2023 (2023)Lian, Y., Gómez, G., Masdemont, J.J., et al.: A note on the dynamics around the lagrange collinear points of the earth-moon system in a complete solar system model. Celest. Mech. Dyn. Astron. 115, 185–211 (2013). ADS MathSciNet MATH Google Scholar McCarthy, B.P., Howell, K.C.: Leveraging quasi-periodic orbits for trajectory design in cislunar space. Astrodynamics 5(2), 139–165 (2021). ADS MATH Google Scholar Meyer, K.R., Offin, D.C.: Introduction to hamiltonian dynamical systems and the N-body problem. Springer International Publishing (2018). L., Kevorkin, J.: Some limiting cases of the restricted four-body problem. Astron. J. 72(8), 959–963 (1967). ADS MATH Google Scholar Olikara, Z.P., Howell, K.C.: Computation of quasi-periodic invariant tori in the restricted three-body problem. In: 20th AAS/AIAA Space Flight Mechanics Meeting, San Diego, California (2010)Olikara, Z.P., Scheeres, D.J.: Numerical method for computing quasi-periodic orbits and their stability in the restricted three-body problem. Adv. Astronaut. Sci. 145(911–930), 911–930 (2012)MATH Google Scholar Olikara, Z.P., Scheeres, D.J.: Mapping connections between planar sun-earth-moon libration orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting, American Astronautical Society San Antonio, Texas (2017)Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun–Earth–Moon Collinear Libration Points. In: Astrodynamics Network AstroNet-II. Springer International Publishing, pp 183–192, (2016)Park, B., Howell, K.: Characterizing transition-challenging regions leveraging the elliptic restricted three-body problem: L2 halo orbits. In: AIAA SCITECH 2024 Forum, (2024a)Park, B., Howell, K.C.: Leveraging the elliptic restricted three-body problem for characterization of multi-year earth-moon L\(_2\) halos in an ephemeris model. In: AAS/AIAA Astrodynamics Specialist Conference, Big Sky, Montana, August 13-17, 2023 (2023)Park, B., Howell, K.C.: Assessment of dynamical models for transitioning from the circular restricted three-body problem to an ephemeris model with applications. Celestial Mech. Dyn. Astron. (2024b)Park, R.S., Folkner, W.M., Williams, J.G., et al.: The jpl planetary and lunar ephemerides de440 and de441. Astron. J. 161(3), 105 (2021). ADS Google Scholar Peng, H., Xu, S.: Stability of two groups of multi-revolution elliptic halo orbits in the elliptic restricted three-body problem. Celest. Mech. Dyn. Astron. 123(3), 279–303 (2015). ADS MathSciNet MATH Google Scholar Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth-Moon L\(_1\) and L\(_2\) in the Hill restricted 4-body problem. Physica D 455(133), 889 (2023). MATH Google Scholar Rosales, J.J., Jorba, A., Jorba-Cuscó, M.: Families of Halo-like invariant tori around \(L_2\) in the Earth-Moon Bicircular Problem. Celest. Mech. Dyn. Astron. 133(4), 16 (2021). ADS MATH Google Scholar Rosales, J.J.,

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By Kate Sotir, Cooper Sarafin, Anderson Fan, Shep Green, VI Form and Mo Liu, V FormMath Modeling: Using Math for Flight Path SafetyPart 1: The problem at hand is to create a model, a rating system, that would inform potential flyers of the safety of a particular flight. Our solution includes a mathematical equation that gives us a number between 1 and 100, depending on the inputs. Although the values themselves indicate the safety level of flights, we do not want to our audience to read into the numbers: a flight with a safety index of 63 should not be considered a more dangerous flight than a flight with a safety index of 67. Therefore, to make our model directly presentable to our audience, we classified the possible outcomes into ratings. A safety index ranges from 1 to 20 would have a rating of ★, from 20 to 40 would have ★★, 40 to 60 would be ★★★, 60 to 80 ★★★★, and finally, 80 to 100 would have the highest rating of ★★★★★, and flights that fall under this rating would be the safest choice based on our model.One major assumption that we made during the creation of our model was assuming that there is no possibility of human error involved in any of the flights that we model. However, in reality, most major plane crashes are caused by errors of the pilot. We chose to make this assumption because of our given time restraint and the amount of resources that we had at our disposal. It was not realistic to fully examine each pilot and record the possibility of human error. Since we do not have access to the information of each individual pilot, we assume that the longer the flight, the more tired the pilots get on the plane and, therefore, the more dangerous the flight gets. Relating again to the path of the flight, we assumed that it is easier to fly over water than it is over mountains. Although none of us have ever flown a plane, we agreed that mountains would make a flight more difficult to maneuver. Another assumption is that all of the aircraft being used were fully functional, regularly examined, and fully repaired. Again, we made an assumption about the sturdiness of the plane because we cannot check each individual plane’s safety. However, we do have fatality rates of each particular type of aircraft given by the companies.Our model consists of five main variables: time of day, weather conditions, aircraft type, the difficulty of the flight route, and the airline company’s safety index. The first factor, time of day, is less correlated with time than the visibility. According to data, although. Download the latest version of Math Flight for Android. Math Flight is a game where players complete path by solving math. Math Flight is an engaging and Download the APK of Math Flight for Android for free. Math Flight is a game where players complete path by solving math. Math Flight is an engaging and

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