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 consid...
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crioppubl:10.1088/1742-6596/1391/1/012137 2024-06-02T08:15:26+00:00 Simulation of motion of satellites after fixing the values of their accelerations Mazitov, K D Yushkov, M P 2019 http://dx.doi.org/10.1088/1742-6596/1391/1/012137 https://iopscience.iop.org/article/10.1088/1742-6596/1391/1/012137/pdf https://iopscience.iop.org/article/10.1088/1742-6596/1391/1/012137 unknown IOP Publishing http://creativecommons.org/licenses/by/3.0/ https://iopscience.iop.org/info/page/text-and-data-mining Journal of Physics: Conference Series volume 1391, issue 1, page 012137 ISSN 1742-6588 1742-6596 journal-article 2019 crioppubl https://doi.org/10.1088/1742-6596/1391/1/012137 2024-05-07T14:01:49Z 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. Article in Journal/Newspaper Tundra IOP Publishing Lagrange ENVELOPE(-62.597,-62.597,-64.529,-64.529) Journal of Physics: Conference Series 1391 1 012137 |
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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. |
format |
Article in Journal/Newspaper |
author |
Mazitov, K D Yushkov, M P |
spellingShingle |
Mazitov, K D Yushkov, M P Simulation of motion of satellites after fixing the values of their accelerations |
author_facet |
Mazitov, K D Yushkov, M P |
author_sort |
Mazitov, K D |
title |
Simulation of motion of satellites after fixing the values of their accelerations |
title_short |
Simulation of motion of satellites after fixing the values of their accelerations |
title_full |
Simulation of motion of satellites after fixing the values of their accelerations |
title_fullStr |
Simulation of motion of satellites after fixing the values of their accelerations |
title_full_unstemmed |
Simulation of motion of satellites after fixing the values of their accelerations |
title_sort |
simulation of motion of satellites after fixing the values of their accelerations |
publisher |
IOP Publishing |
publishDate |
2019 |
url |
http://dx.doi.org/10.1088/1742-6596/1391/1/012137 https://iopscience.iop.org/article/10.1088/1742-6596/1391/1/012137/pdf https://iopscience.iop.org/article/10.1088/1742-6596/1391/1/012137 |
long_lat |
ENVELOPE(-62.597,-62.597,-64.529,-64.529) |
geographic |
Lagrange |
geographic_facet |
Lagrange |
genre |
Tundra |
genre_facet |
Tundra |
op_source |
Journal of Physics: Conference Series volume 1391, issue 1, page 012137 ISSN 1742-6588 1742-6596 |
op_rights |
http://creativecommons.org/licenses/by/3.0/ https://iopscience.iop.org/info/page/text-and-data-mining |
op_doi |
https://doi.org/10.1088/1742-6596/1391/1/012137 |
container_title |
Journal of Physics: Conference Series |
container_volume |
1391 |
container_issue |
1 |
container_start_page |
012137 |
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1800739611062829056 |