2023; Physical and Mathematical Sciences, 57(2 (261): 51–61
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ON OPTIMAL STABILIZATION OF PART OF VARIABLES OF ROTARY MOVEMENT OF A RIGID BODY WITH ONE FIXED POINT IN THE CASE OF SOPHIA KOVALEVSKAYA

Smbat Shahinyan*

Received: 2025-01-21 · Published: 2023-08-12

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CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
ON OPTIMAL STABILIZATION OF PART OF VARIABLES OF ROTARY MOVEMENT OF A RIGID BODY WITH ONE FIXED POINT IN THE CASE OF SOPHIA KOVALEVSKAYA
Author
Smbat Shahinyan
Published
2023-08-12
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2023.57.2.051

Abstract

of a rigid body with one fixed point in the Sophia Kovalevskaya's case is discussed in this work. The differential equations of motion of the system are given and it is shown that the system may rotate around Ox with a constant angular velocity. Taking this motion as unexcited, the differential equations for the corresponding excited motion were drawn up. Then the system was linearized and a control action was introduced along one of the generalized coordinates. The optimal stabilization problem for part of the variables was posed and solved. The graphs of optimal trajectories and optimal control were constructed.
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