Simulation of motion of satellites after fixing the values of their accelerations

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Simulation of motion of satellites after fixing the values of their accelerations. / Mazitov, K. D.; Yushkov, M. P.

In: Journal of Physics: Conference Series, Vol. 1391, No. 1, 012137, 13.12.2019.

Research output: Contribution to journal › Conference article › peer-review

BibTeX

@article{ed59b9a04f2d49ceb11864cfaea9596f,

title = "Simulation of motion of satellites after fixing the values of their accelerations",

abstract = "At the Department of Theoretical and Applied Mechanics of the Faculty of Mathematics and Mechanics of St. Petersburg State University [1] the theory of motion of nonholonomic systems with linear nonholonomic constraints of high order n<2 was created. The high-order constraints are considered as program and ideal ones, and their reaction force is considered as the required control force. A consistent system of differential equations with respect to unknown generalized coordinates and Lagrange multipliers is constructed to solve the problem. The report examines the motion of Soviet satellites of the systems {"}Cosmos{"}, {"}Molniya{"}, {"}Tundra{"} after fixing the values of their accelerations in apogees. This corresponds to imposing the nonlinear second-order nonholonomic constraints on the further motion of satellites [2, 3]. The equations of constraints are differentiated in time and presented as linear third-order constraints to make it possible to apply the above theory. The motions of satellites are studied in polar coordinates, the origin of this system coinciding with the center of the Earth. It turns out that after fixing the acceleration values in the apogees, the satellites begin to rotate between two concentric circles, alternately touching each of them.",

author = "Mazitov, {K. D.} and Yushkov, {M. P.}",

note = "Publisher Copyright: {\textcopyright} 2019 IOP Publishing Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; 8th International Conference on Mathematical Modeling in Physical Science, IC-MSQUARE 2019 ; Conference date: 26-08-2019 Through 29-08-2019",

year = "2019",

month = dec,

day = "13",

doi = "10.1088/1742-6596/1391/1/012137",

language = "English",

volume = "1391",

journal = "Journal of Physics: Conference Series",

issn = "1742-6588",

publisher = "IOP Publishing Ltd.",

number = "1",

}

RIS

TY - JOUR

T1 - Simulation of motion of satellites after fixing the values of their accelerations

AU - Mazitov, K. D.

AU - Yushkov, M. P.

PY - 2019/12/13

Y1 - 2019/12/13

N2 - At the Department of Theoretical and Applied Mechanics of the Faculty of Mathematics and Mechanics of St. Petersburg State University [1] the theory of motion of nonholonomic systems with linear nonholonomic constraints of high order n<2 was created. The high-order constraints are considered as program and ideal ones, and their reaction force is considered as the required control force. A consistent system of differential equations with respect to unknown generalized coordinates and Lagrange multipliers is constructed to solve the problem. The report examines the motion of Soviet satellites of the systems "Cosmos", "Molniya", "Tundra" after fixing the values of their accelerations in apogees. This corresponds to imposing the nonlinear second-order nonholonomic constraints on the further motion of satellites [2, 3]. The equations of constraints are differentiated in time and presented as linear third-order constraints to make it possible to apply the above theory. The motions of satellites are studied in polar coordinates, the origin of this system coinciding with the center of the Earth. It turns out that after fixing the acceleration values in the apogees, the satellites begin to rotate between two concentric circles, alternately touching each of them.

AB - At the Department of Theoretical and Applied Mechanics of the Faculty of Mathematics and Mechanics of St. Petersburg State University [1] the theory of motion of nonholonomic systems with linear nonholonomic constraints of high order n<2 was created. The high-order constraints are considered as program and ideal ones, and their reaction force is considered as the required control force. A consistent system of differential equations with respect to unknown generalized coordinates and Lagrange multipliers is constructed to solve the problem. The report examines the motion of Soviet satellites of the systems "Cosmos", "Molniya", "Tundra" after fixing the values of their accelerations in apogees. This corresponds to imposing the nonlinear second-order nonholonomic constraints on the further motion of satellites [2, 3]. The equations of constraints are differentiated in time and presented as linear third-order constraints to make it possible to apply the above theory. The motions of satellites are studied in polar coordinates, the origin of this system coinciding with the center of the Earth. It turns out that after fixing the acceleration values in the apogees, the satellites begin to rotate between two concentric circles, alternately touching each of them.

UR - http://www.scopus.com/inward/record.url?scp=85077820561&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1391/1/012137

DO - 10.1088/1742-6596/1391/1/012137

M3 - Conference article

AN - SCOPUS:85077820561

VL - 1391

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012137

T2 - 8th International Conference on Mathematical Modeling in Physical Science, IC-MSQUARE 2019

Y2 - 26 August 2019 through 29 August 2019

ER -

ID: 71880363