ON OPTIMAL STABILIZATION OF PART OF VARIABLES OF ROTARY MOVEMENT OF A RIGID BODY WITH ONE FIXED POINT IN THE CASE OF SOPHIA KOVALEVSKAYA

Authors

  • Smbat G. Shahinyan Chair of Mechanics, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2023.57.2.051

Keywords:

rigid body, optimal control, optimal stabilization

Abstract

An optimal stabilization problem for part of variables of rotary movement 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.

References

Buchholz N.N. The Main Course of Theoretical Mechanics. Part 2. Moskow, Nauka, (1972), 332 (in Russian).

Shahinyan S.G., Avetisyan L.M. On One Problem of Optimal Stabilization of the Rotational Motion of a Rigid Body Having a Fixed Point. Proceedings of the IX International Conference ``Problems of the Dynamics of Interaction of Deformable Media. Armenia, Goris (2018), 306-310.

Malkin I.G. Theory of Motion of Stability. Moskow, Nauka (1966), 475-514 (in Russian).

Krasovsky N.N. Some Tasks of the Theory of Motion Control. Moskow, Nauka (1968), 475 (in Russian).

Rumyantsev V.V., Oziraner A.S. Stability and Stabilization of Movement in Relation to Part of the Variables. Moskow, Nauka (1987), 256 (in Russian).

Krasovsky N.N. Problems of Stabilization of Controlled Motions. In Book: Theory of Motion of Stability (ed. I.G. Malkin Add. 4). Moskow, Nauka (1966), 475-515 (in Russian).

Al'brecht E.G., Shelementiev G.S. Lectures on the Theory of Stabilization. Sverdlovsk (1972), 274 (in Russian).

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Published

2023-07-12

How to Cite

Shahinyan, S. G. (2023). ON OPTIMAL STABILIZATION OF PART OF VARIABLES OF ROTARY MOVEMENT OF A RIGID BODY WITH ONE FIXED POINT IN THE CASE OF SOPHIA KOVALEVSKAYA. Proceedings of the YSU A: Physical and Mathematical Sciences, 57(2 (261), 51–61. https://doi.org/10.46991/PYSU:A/2023.57.2.051

Issue

Section

Mechanics