Analytical approximation of inertial manifolds for the satellite motion model


DOI: 10.34759/trd-2022-123-25

Аuthors

Kondratieva L. A.

e-mail: liudmila.kondratieva@inbox.ru

Keywords:

satellite motion model; inertial manifold; stable limit cycle

References

  1. Panteleev A., Karane M. Hybrid multi-agent optimization method of interpolation search, AIP Conference Proceedings, 2019, no. 2181 (1), pp. 020028. DOI:10.1063/1.5135688

  2. Averina T., Rybakov K. Systems with regime switching on manifolds // Proceedings of the 2018 14th International Conference “Stability and Oscillations of Nonlinear Control Systems” (Pyatnitskiy’s Conference) (STAB), IEEE, 2018, pp. 1-3. DOI:10.1109/STAB.2018.8408345

  3. Bortakovskii A.S., Uryupin I.V. Trudy MAI, 2020, no. 113. URL: http://trudymai.ru/eng/published.php?ID=118185. DOI: 10.34759/trd-2020-113-17

  4. Semenov V.V., Panteleev A.V., Bortakovskii A.S. Matematicheskaya teoriya upravleniya v primerakh i zadachakh (Mathematical theory of control in examples and problems), Moscow, Izd-vo MAI-Print, 1997, 264 p.

  5. Sidorenko V.V., Celletti A. “Spring-mass” model of tethered satellite systems: properties of planar periodic motions, Celestial Mechanics and Dynamical Astronomy, 2010, no. 107 (1-2), pp. 209-231. DOI:10.1007/s10569-010-9275-5

  6. Galiullin I.A., Kondrat'eva L.A. Kosmonavtika i raketostroenie, 2011, no. 3 (64), pp. 73-76.

  7. Kondrat'eva L.A. Aerospace MAI Journal, 2012, vol. 19, no. 1, pp. 75-80.

  8. Kondratieva L. Computational model for satellite periodic motion, In 21st International Conference on Computational Mechanics and Modern Applied Software Systems, CMMASS-2019, AIP Conference Proceedings 2181 020002, AIP Publishing, 2019. DOI:10.1063/1.5135662

  9. Kondratieva L.A., Romanov A.V. Inertial manifolds and limit cycles of dynamical systems in R n, Electronic Journal of Qualitative Theory of Differential Equations, 2019, no. 96, pp. 1-11.

  10. Khrustalev M.M., Khalina A.S. Trudy MAI, 2018, no. 102. URL: http://trudymai.ru/eng/published.php?ID=99065

  11. Kazmerchuk P.V., Vernigora L.V. Trudy MAI, 2020, no. 115. URL: http://trudymai.ru/eng/published.php?ID=119924. DOI: 10.34759/trd-2020-115-09

  12. Panteleev A.V., Karane M.M.S. Trudy MAI, 2021, no. 117. URL: http://trudymai.ru/eng/published.php?ID=156249. DOI: 10.34759/trd-2021-117-10

  13. Abouelmagd E.I., Doshi M.J., Pathak N.M. Evolution of Periodic Orbits within the Frame of Formation Satellites, Advances in Astronomy, 2020, vol. 3, pp. 1-17. DOI: 10.1155/2020/1348319

  14. Pal A.K., Abouelmagd E.I., García Guirao J.L., Brzezinski D.W. Periodic Solutions of Nonlinear Relative Motion Satellites, Symmetry, 2021, no. 13 (595), pp. 1-20. DOI: 10.3390/sym13040595

  15. Temam R. Infinite-dimensional dynamical systems in mechanics and physics (Second ed.). Springer, New York, 1997, 648 p.

  16. Ito K., Kunisch K. Reduced-order optimal control based on approximate inertial manifolds for nonlinear dynamical systems. SIAM Journal on Numerical Analysis, 2008, no. 46 (6), pp. 2867-2891. DOI:10.1016/j.laa.2004.10.019

  17. Zhang J.-Z., Liu Y., Feng P.-H. Approximate inertial manifolds of Burgers equation approached by nonlinear Galerkin’s procedure and its application, Comm. in Nonlinear Science and Numerical Simulation, 2011, no. 16 (12), pp. 4666-4670. DOI:10.1016/j.cnsns.2011.03.004

  18. Debussche A., Temam R. Convergent families of approximate inertial manifolds, Journal de Mathématiques Pures et Appliquées, 1994, no. 73, pp. 485-522.

  19. Lisha Xu, Hua Deng, Chong Lin, Yi Zhang. Approximate Inertial Manifold-Based Model Reduction and Vibration Suppression for Rigid-Flexible Mechanical Arms, Complexity, 2021, pp. 1–17. URL: DOI: 10.1155/2021/8290978

  20. Poland D. Loci of limit cycles, Physical Review E, 1994. no. 49 (1), pp.157-165. DOI:10.1103/PHYSREVE.49.157

  21. Delamotte B. Nonperturbative (but approximate) method for solving differential equations and finding limit cycles, Physical Review Letters, 1993, no.70 (22), pp. 3361-3364. DOI:10.1103/PHYSREVLETT.70.3361


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