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

In: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, Vol. 13, No. 1, 2017, p. 102-112.

Research output: Contribution to journal › Article › peer-review

Harvard

Maliavkin, GP, Shmyrov, VA & Shmyrov, AS 2017, 'Design of the stabilizing control of the orbital motion using the analytical representation of an invariant manifold in the vicinity of a collinear libration point', Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, vol. 13, no. 1, pp. 102-112. https://doi.org/10.21638/11701/spbu10.2017.110

APA

Maliavkin, G. P., Shmyrov, V. A., & Shmyrov, A. S. (2017). Design of the stabilizing control of the orbital motion using the analytical representation of an invariant manifold in the vicinity of a collinear libration point. Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, 13(1), 102-112. https://doi.org/10.21638/11701/spbu10.2017.110

Vancouver

Maliavkin GP, Shmyrov VA, Shmyrov AS. Design of the stabilizing control of the orbital motion using the analytical representation of an invariant manifold in the vicinity of a collinear libration point. Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya. 2017;13(1):102-112. https://doi.org/10.21638/11701/spbu10.2017.110

Author

Maliavkin, G. P. ; Shmyrov, V. A. ; Shmyrov, A. S. / Design of the stabilizing control of the orbital motion using the analytical representation of an invariant manifold in the vicinity of a collinear libration point. In: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya. 2017 ; Vol. 13, No. 1. pp. 102-112.

BibTeX

@article{4bcb3bf5df044850a9b9fe01bfb8bb59,
title = "Design of the stabilizing control of the orbital motion using the analytical representation of an invariant manifold in the vicinity of a collinear libration point",
abstract = "The article is devoted to the problem of stabilization of orbital motion in the vicinity of the collinear libration point L1 of the Sun - Earth system. The key concept of the suggested approach is the so-called hazard function. The latter is a function of the phase variables of the Hill's approximation of the circular restricted three-body problem, which is defined as a nondegenerate solution of some partial differential equation. The hazard function can be used for the analytical representation of an invariant manifold in the vicinity of the libration point. Approximations of the hazard function of the first, second and the third order are obtained with the method of indefinite coefficients. These approximations are then used in the construction of three motion stabilizing control laws. Numerical modelling of the controlled motion is applied to compare these laws with respect to the energy consumptions.",
keywords = "Collinear libration point, Invariant manifold, Restricted three-body problem, Stabilizing control of motion",
author = "Maliavkin, {G. P.} and Shmyrov, {V. A.} and Shmyrov, {A. S.}",
year = "2017",
doi = "10.21638/11701/spbu10.2017.110",
language = "English",
volume = "13",
pages = "102--112",
journal = " ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ",
issn = "1811-9905",
publisher = "Издательство Санкт-Петербургского университета",
number = "1",

}

RIS

TY - JOUR

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

AU - Maliavkin, G. P.

AU - Shmyrov, V. A.

AU - Shmyrov, A. S.

PY - 2017

Y1 - 2017

N2 - The article is devoted to the problem of stabilization of orbital motion in the vicinity of the collinear libration point L1 of the Sun - Earth system. The key concept of the suggested approach is the so-called hazard function. The latter is a function of the phase variables of the Hill's approximation of the circular restricted three-body problem, which is defined as a nondegenerate solution of some partial differential equation. The hazard function can be used for the analytical representation of an invariant manifold in the vicinity of the libration point. Approximations of the hazard function of the first, second and the third order are obtained with the method of indefinite coefficients. These approximations are then used in the construction of three motion stabilizing control laws. Numerical modelling of the controlled motion is applied to compare these laws with respect to the energy consumptions.

AB - The article is devoted to the problem of stabilization of orbital motion in the vicinity of the collinear libration point L1 of the Sun - Earth system. The key concept of the suggested approach is the so-called hazard function. The latter is a function of the phase variables of the Hill's approximation of the circular restricted three-body problem, which is defined as a nondegenerate solution of some partial differential equation. The hazard function can be used for the analytical representation of an invariant manifold in the vicinity of the libration point. Approximations of the hazard function of the first, second and the third order are obtained with the method of indefinite coefficients. These approximations are then used in the construction of three motion stabilizing control laws. Numerical modelling of the controlled motion is applied to compare these laws with respect to the energy consumptions.

KW - Collinear libration point

KW - Invariant manifold

KW - Restricted three-body problem

KW - Stabilizing control of motion

UR - http://www.scopus.com/inward/record.url?scp=85031114964&partnerID=8YFLogxK

U2 - 10.21638/11701/spbu10.2017.110

DO - 10.21638/11701/spbu10.2017.110

M3 - Article

AN - SCOPUS:85031114964

VL - 13

SP - 102

EP - 112

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 1

ER -

ID: 9180776