The influence of jump conditions in conjugate variables on the multiorbit spacecraft transfers with switching the low thrust off in the Earth's shadow

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅或者付费存取

详细

Transfers in the central Newtonian field to the geostationary orbit are considered under the assumption that low thrust becomes zero when spacecraft with solar panels enters the Earth’s shadow. Using the maximum principle, the two-point boundary value problem is formed. It includes the conditions for optimal intersection of the shadow boundaries, the so called jump conditions in conjugate variables. Then the influence of jump conditions on the two-point boundary value problem solutions is investigated. Calculations for the flights of spacecraft with initial mass 5550 kg and thrust 0.55 N (initial acceleration 0.1 mm/s2) from the initial orbit with inclination 13° and the height of perigee 9.2 Mm and of apogee 76.8 Mm were done. They showed that if the argument of pericenter is equal to 0° and the longitude of the ascending node Ω0 = 180°, the difference in the propellant cost for two trajectories – with or without taking into account the jump conditions – does not exceed 0.15 % (in comparison with “nominal” trajectories, i.e., transfers without zeroing the thrust), and may be less than 0.01 % for some values of initial time. For other values of Ω0, the difference may be greater than 30 %. It was discovered also that the two-point boundary value problem may have several solutions. They differ from each other by the set of orbits crossing the Earth’s shadow.

全文:

受限制的访问

作者简介

R. Akhmetshin

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences

编辑信件的主要联系方式.
Email: axmetro@yandex.ru
俄罗斯联邦, Moscow

参考

  1. Shirazi A., Ceberio J., Lozano J.A. Spacecraft trajectory optimization: A review of models, objectives, approaches and solutions // Progress in Aerospace Sciences. 2018. V. 102. P. 76–98.
  2. Graham K.F., Rao A.V. Minimum-Time Trajectory Optimization of Low-Thrust Earth-Orbit Transfers with Eclipsing // J. Spacecraft and Rockets. 2016. V. 53. Iss. 2. P. 289–303. https://doi.org/10.2514/1.A33416
  3. Wang Y., Topputo F. Indirect Optimization for Low-Thrust Transfers with Earth-Shadow Eclipses // Advances in the Astronautical Sciences AAS/AIAA Spaceflight Mechanics. 2021. V. 176.
  4. Понтрягин Л.С., Болтянский В.Г., Гамкрелидзе Р.В. и др. Математическая теория оптимальных процессов. М.: Наука, 1976.
  5. Ferrier Ch., Epenoy R. Optimal control for engines with electro-ionic propulsion under constraint of eclipse // Acta Astronautica. 2001. V. 48. Iss. 4. P. 181–192. https://doi.org/10.1016/S0094-5765(00)00158-2
  6. Woollands R., Taheri E. Optimal Low-Thrust Gravity Perturbed Orbit Transfers with Shadow Constraints // The 2019 AAS/AIAA Astrodynamics Specialist Conference. Portland, Maine. 2019.
  7. Cerf M. Fast Solution of Minimum-Time Low-Thrust Transfer with Eclipses // Proc. Institution of Mechanical Engineers. Part G: J. Aerospace Engineering. 2019. V. 233. Iss. 7. P. 2699–2714. https://doi.org/10.1177/0954410018785971
  8. Pontani M., Corallo F. Optimal Low-Thrust Lunar Orbit Transfers with Shadowing Effect Using a Multiple-Arc Formulation // Acta Astronautica. 2022. V. 200. Iss. 11. P. 549–561.
  9. Pontani M., Corallo F. Optimal Low-Thrust Earth Orbit Transfers with Eclipses Using Indirect Heuristic Approaches // J. Guidance, Control and Dynamics. 2024. V. 47. Iss. 5. P. 857–873. https://doi.org/10.2514/1.G007797
  10. Ахметшин Р.З. Плоская задача оптимального перелета космического аппарата с малой тягой с высокоэллиптической орбиты на геостационар // Космич. исслед. 2004. T. 42. № 3. C. 248–259; Akhmetshin R.Z. Planar Problem of an Optimal Transfer of a Low-Thrust Spacecraft from High-Elliptic to Geosynchronous Orbit. Cosmic Research. 2004. V. 42. Iss. 3. P. 238–249.
  11. Ахметшин Р.З. Многовитковые перелеты на геостационарную орбиту с обнулением малой тяги в области тени // Космич. исслед. 2020. T. 58. № 4. C. 321–330. https://doi.org/10.31857/S0023420620040019; Akhmetshin R.Z. Multiorbit Transfers to a Geostationary Orbit with Switching Low Thrust Off in the Shadow Region // Cosmic Research. 2020. V. 58. Iss. 4. P. 285–294). https://doi.org/10.1134/S0010952520040012
  12. Ахметшин Р.З. Влияние возмущений при многовитковых перелетах на геостационарную орбиту // Космич. исслед. 2021. T. 59. № 5. C. 377–384. https://doi.org/10.31857/S0023420621050010; Akhmetshin R.Z. The Influence of Disturbances during Multiturn Transfer to a Geostationary Orbit // Cosmic Research. 2021. V. 59. Iss. 5. P. 328–334). https://doi.org/10.1134/S0010952521050014
  13. Петухов В.Г. Оптимизация многовитковых перелетов между некомпланарными эллиптическими орбитами // Космич. исслед. 2004. Т. 42. № 3. C. 260–279; Petukhov V.G. Optimization of multi-orbit transfers between noncoplanar elliptic orbits // Cosmic Research. 2004. V. 42. Iss. 3. P. 250–268
  14. Петухов В.Г. Квазиоптимальное управление с обратной связью для многовиткового перелета с малой тягой между некомпланарными эллиптической и круговой орбитами // Космич. исслед. 2011. Т. 49. № 2. С. 128–137; Petukhov V.G. Quasioptimal control with feedback for multiorbit low-thrust transfer between noncoplanar elliptic and circular orbits // Cosmic Research. 2011. V. 49. Iss. 2. P. 121–130.
  15. Caillau J.B., Gergaud J., Noailles J. 3D Geosynchronous Transfer of a Satellite: Continuation on the Thrust // J. Optimization Theory and Applications. 2003. V. 118. Iss. 3. P. 541–565.
  16. Ким В.П., Гниздор Р.Ю., Грдличко Д.П. и др. Разработка стационарного плазменного двигателя СПД-100Вт с повышенной тягой // Космич. исслед. 2019. T. 57. № 5. C. 323–331. https://doi.org/10.1134/S0023420619050030

补充文件

附件文件
动作
1. JATS XML
下载
2. Fig. 1. Model of a “cylindrical” shadow

下载 (17KB)
索引源数据
3. Fig. 2. Nominal trajectory projected onto the equatorial plane in the celestial coordinate system: X(t) = r (cosu×cosΩ – sinu sinΩ×cosi), Y(t) = r (cosu×sinΩ + sinu cosΩ×cosi, u = ω + θ). Turns 1, 11…151, 157 are drawn. The shadow areas on the trajectory are numbered (1, 2, 3) for three values of t0: 0, 90 and 180 days, respectively. At t0 = 0 days, there are 50 shadow areas; at t0 = 180 days, there are 21 areas; at t0 = 90 days, there are two groups of 21 areas at the beginning and 24 areas at the end of the trajectory.

下载 (44KB)
索引源数据
4. Fig. 3. Solutions (with best N) of incomplete and complete two-point boundary value problems

下载 (13KB)
索引源数据
5. Fig. 4. Groups of turns with or without shadow on nominal trajectories depending on t0. The trajectories are divided into 8 classes by the number and type of groups of turns.

下载 (47KB)
索引源数据
6. Fig. 5. Enlarged part of the graphs from Fig. 3 near the abscissa axis

下载 (14KB)
索引源数据
7. Fig. 6. Solutions of the incomplete boundary value problem and a series of solutions of the complete two-point boundary value problem for Ω0 = 260° and t0 ∈ [0…95] days and [275…365] days

下载 (15KB)
索引源数据
8. Fig. 7. Enlarged part of the graphs from Fig. 6 near the abscissa axis and the solution of the complete boundary value problem for t0 ∈ [100…270] days

下载 (15KB)
索引源数据
9. Fig. 8. Solutions of an incomplete and two series of solutions of a complete two-point boundary value problem

下载 (16KB)
索引源数据
10. Fig. 9. Two graphs from Fig. 8 and a series of solutions of the complete boundary value problem with the best number of turns N on an enlarged scale

下载 (15KB)
索引源数据
11. Fig. 10. Best solutions of complete and incomplete two-point boundary value problems for Ω0 = 300°

下载 (15KB)
索引源数据
12. Fig. 11. The best solutions of the complete and incomplete two-point boundary value problems for Ω0 = 260°. For comparison, the initially obtained solutions of the complete boundary value problem from Fig. 7 are also shown as black dots. The difference between the two solutions for t0 = 120 days is that on the best trajectory there are areas with a shadow on orbits 1–22, 108–145, on the second trajectory — on orbits 1–22, 107–145; for t0 = 180 days — respectively on orbits 61–92 and 60–93; for t0 = 240 days — on orbits 18–46 and 17–47.

下载 (16KB)
索引源数据
13. Fig. 12. The best solutions of complete and incomplete two-point boundary value problems for Ω0 = 40°

下载 (17KB)
索引源数据
14. Fig. 13. Best solutions of complete and incomplete two-point boundary value problems for Ω0 = 180°

下载 (15KB)
索引源数据

版权所有 © Russian Academy of Sciences, 2025