Standard

Design of the stabilizing control of the orbital motion in the vicinity of the collinear libration point L1 using the analytical representation of the invariant manifold. / Maliavkin, G. P.; Shmyrov, A. S.; Shmyrov, V. A.

EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics. ed. / Elena V. Kustova; Gennady A. Leonov; Mikhail P. Yushkov; Nikita F. Morosov; Mariia A. Mekhonoshina. Vol. 1959 American Institute of Physics, 2018. 040010 (AIP Conference Proceedings; Vol. 1959).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Harvard

Maliavkin, GP, Shmyrov, AS & Shmyrov, VA 2018, Design of the stabilizing control of the orbital motion in the vicinity of the collinear libration point L1 using the analytical representation of the invariant manifold. in EV Kustova, GA Leonov, MP Yushkov, NF Morosov & MA Mekhonoshina (eds), EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics. vol. 1959, 040010, AIP Conference Proceedings, vol. 1959, American Institute of Physics, International Scientific Conference on Mechanics - Eighth Polyakhov's Reading, Saint Petersburg, Russian Federation, 29/01/18. https://doi.org/10.1063/1.5034613

APA

Maliavkin, G. P., Shmyrov, A. S., & Shmyrov, V. A. (2018). Design of the stabilizing control of the orbital motion in the vicinity of the collinear libration point L1 using the analytical representation of the invariant manifold. In E. V. Kustova, G. A. Leonov, M. P. Yushkov, N. F. Morosov, & M. A. Mekhonoshina (Eds.), EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics (Vol. 1959). [040010] (AIP Conference Proceedings; Vol. 1959). American Institute of Physics. https://doi.org/10.1063/1.5034613

Vancouver

Maliavkin GP, Shmyrov AS, Shmyrov VA. Design of the stabilizing control of the orbital motion in the vicinity of the collinear libration point L1 using the analytical representation of the invariant manifold. In Kustova EV, Leonov GA, Yushkov MP, Morosov NF, Mekhonoshina MA, editors, EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics. Vol. 1959. American Institute of Physics. 2018. 040010. (AIP Conference Proceedings). https://doi.org/10.1063/1.5034613

Author

Maliavkin, G. P. ; Shmyrov, A. S. ; Shmyrov, V. A. / Design of the stabilizing control of the orbital motion in the vicinity of the collinear libration point L1 using the analytical representation of the invariant manifold. EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics. editor / Elena V. Kustova ; Gennady A. Leonov ; Mikhail P. Yushkov ; Nikita F. Morosov ; Mariia A. Mekhonoshina. Vol. 1959 American Institute of Physics, 2018. (AIP Conference Proceedings).

BibTeX

@inproceedings{3f067597d6064df4abbe2a72f58d2119,
title = "Design of the stabilizing control of the orbital motion in the vicinity of the collinear libration point L1 using the analytical representation of the invariant manifold",
abstract = "Vicinities of collinear libration points of the Sun-Earth system are currently quite attractive for the space navigation. Today, various projects on placing of spacecrafts observing the Sun in the L1 libration point and telescopes in L2 have been implemented (e.g. spacecrafts {"}WIND{"}, {"}SOHO{"}, {"}Herschel{"}, {"}Planck{"}). Collinear libration points being unstable leads to the problem of stabilization of a spacecraft's motion. Laws of stabilizing motion control in vicinity of L1 point can be constructed using the analytical representation of a stable invariant manifold. Efficiency of these control laws depends on the precision of the representation. Within the model of Hill's approximation of the circular restricted three-body problem in the rotating geocentric coordinate system one can obtain the analytical representation of an invariant manifold filled with bounded trajectories in a form of series in terms of powers of the phase variables. Approximate representations of the orders from the first to the fourth inclusive can be used to construct four laws of stabilizing feedback motion control under which trajectories approach the manifold. By virtue of numerical simulation the comparison can be made: how the precision of the representation of the invariant manifold influences the efficiency of the control, expressed by energy consumptions (characteristic velocity). It shows that using approximations of higher orders in constructing the control laws can significantly reduce the energy consumptions on implementing the control compared to the linear approximation.",
author = "Maliavkin, {G. P.} and Shmyrov, {A. S.} and Shmyrov, {V. A.}",
year = "2018",
month = may,
day = "2",
doi = "10.1063/1.5034613",
language = "English",
volume = "1959",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics",
editor = "Kustova, {Elena V.} and Leonov, {Gennady A.} and Yushkov, {Mikhail P.} and Morosov, {Nikita F.} and Mekhonoshina, {Mariia A.}",
booktitle = "EIGHTH POLYAKHOV'S READING",
address = "United States",
note = "International Scientific Conference on Mechanics - Eighth Polyakhov's Reading : 8th Polyakhov's Reading ; Conference date: 29-01-2018 Through 02-02-2018",
url = "https://events.spbu.ru/events/polyakhov_readings, http://nanomat.spbu.ru/en/node/175, http://nanomat.spbu.ru/ru/node/192, http://spbu.ru/news-events/calendar/viii-polyahovskie-chteniya",

}

RIS

TY - GEN

T1 - Design of the stabilizing control of the orbital motion in the vicinity of the collinear libration point L1 using the analytical representation of the invariant manifold

AU - Maliavkin, G. P.

AU - Shmyrov, A. S.

AU - Shmyrov, V. A.

N1 - Conference code: 8

PY - 2018/5/2

Y1 - 2018/5/2

N2 - Vicinities of collinear libration points of the Sun-Earth system are currently quite attractive for the space navigation. Today, various projects on placing of spacecrafts observing the Sun in the L1 libration point and telescopes in L2 have been implemented (e.g. spacecrafts "WIND", "SOHO", "Herschel", "Planck"). Collinear libration points being unstable leads to the problem of stabilization of a spacecraft's motion. Laws of stabilizing motion control in vicinity of L1 point can be constructed using the analytical representation of a stable invariant manifold. Efficiency of these control laws depends on the precision of the representation. Within the model of Hill's approximation of the circular restricted three-body problem in the rotating geocentric coordinate system one can obtain the analytical representation of an invariant manifold filled with bounded trajectories in a form of series in terms of powers of the phase variables. Approximate representations of the orders from the first to the fourth inclusive can be used to construct four laws of stabilizing feedback motion control under which trajectories approach the manifold. By virtue of numerical simulation the comparison can be made: how the precision of the representation of the invariant manifold influences the efficiency of the control, expressed by energy consumptions (characteristic velocity). It shows that using approximations of higher orders in constructing the control laws can significantly reduce the energy consumptions on implementing the control compared to the linear approximation.

AB - Vicinities of collinear libration points of the Sun-Earth system are currently quite attractive for the space navigation. Today, various projects on placing of spacecrafts observing the Sun in the L1 libration point and telescopes in L2 have been implemented (e.g. spacecrafts "WIND", "SOHO", "Herschel", "Planck"). Collinear libration points being unstable leads to the problem of stabilization of a spacecraft's motion. Laws of stabilizing motion control in vicinity of L1 point can be constructed using the analytical representation of a stable invariant manifold. Efficiency of these control laws depends on the precision of the representation. Within the model of Hill's approximation of the circular restricted three-body problem in the rotating geocentric coordinate system one can obtain the analytical representation of an invariant manifold filled with bounded trajectories in a form of series in terms of powers of the phase variables. Approximate representations of the orders from the first to the fourth inclusive can be used to construct four laws of stabilizing feedback motion control under which trajectories approach the manifold. By virtue of numerical simulation the comparison can be made: how the precision of the representation of the invariant manifold influences the efficiency of the control, expressed by energy consumptions (characteristic velocity). It shows that using approximations of higher orders in constructing the control laws can significantly reduce the energy consumptions on implementing the control compared to the linear approximation.

UR - http://www.scopus.com/inward/record.url?scp=85047177217&partnerID=8YFLogxK

U2 - 10.1063/1.5034613

DO - 10.1063/1.5034613

M3 - Conference contribution

AN - SCOPUS:85047177217

VL - 1959

T3 - AIP Conference Proceedings

BT - EIGHTH POLYAKHOV'S READING

A2 - Kustova, Elena V.

A2 - Leonov, Gennady A.

A2 - Yushkov, Mikhail P.

A2 - Morosov, Nikita F.

A2 - Mekhonoshina, Mariia A.

PB - American Institute of Physics

T2 - International Scientific Conference on Mechanics - Eighth Polyakhov's Reading

Y2 - 29 January 2018 through 2 February 2018

ER -

ID: 35988243