On first integrals and stability of stationary motions of gyrostat

Kosov, A. A.; Семенов, Е. И.

doi:10.1016/j.physd.2021.133103

Cited by 7 publications

(1 citation statement)

References 16 publications

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“…where L(t, k, π) is an arbitrary function, we obtain the same equilibrium solutions reported in Theorem 1. Furthermore, as proven in [46], ( 7), ( 9) and ( 10) remain as first integrals and the stability results are also valid for this generalized system.…”

Section: Remarksupporting

confidence: 56%

Stability Conditions for Permanent Rotations of a Heavy Gyrostat with Two Constant Rotors

et al. 2022

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In this paper, we consider the motion of an asymmetric heavy gyrostat, when its center of mass lies along one of the principal axes of inertia. We determine the possible permanent rotations and, by means of the Energy-Casimir method, we give sufficient stability conditions. We prove that there exist permanent stable rotations when the gyrostat is oriented in any direction of the space, by the action of two spinning rotors, one of them aligned along the principal axis, where the center of mass lies. We also derive necessary stability conditions that, in some cases, are the same as the sufficient ones.

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Section: Remarksupporting

confidence: 56%

Stability Conditions for Permanent Rotations of a Heavy Gyrostat with Two Constant Rotors

et al. 2022

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On the Integrability and Stability of Stationary Solutions of the Goryachev–Sretensky Gyrostat

Kosov,

Semenov

2023

J. Appl. Ind. Math.

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On the Movement of Gyrostat under the Action of Potential and Gyroscopic Forces

Kosov

Семенов

2022

Zhurnal SVMO

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A system of differential equations is considered that describes the motion of a gyrostat under the action of the moment of potential, gyroscopic and circular-gyroscopic forces. The form of the moment of forces is indicated for which the system has the three first integrals of a given form. An analog of V.I. Zubov’s theorem for representing solutions of gyrostat equations by power series is given, and the possibility of using this approach to predict motions is shown. For an analogue of the Lagrange case, integration in quadratures is performed. Analogues of the case of full dynamical symmetry and the Hess case are also indicated. Based on the principle of optimal damping developed by V.I. Zubov, a design of the control moment created by circular-gyroscopic forces is proposed, which ensures that one of the coordinates reaches a constant (albeit unknown in advance) value or the transition of the state vector to the level surface of the particular Hess integral. A numerical example is given, for which a two-parameter family of exact almost periodic solutions, represented by trigonometric functions, is found.

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On first integrals and stability of stationary motions of gyrostat

Cited by 7 publications

References 16 publications

Stability Conditions for Permanent Rotations of a Heavy Gyrostat with Two Constant Rotors

Stability Conditions for Permanent Rotations of a Heavy Gyrostat with Two Constant Rotors

On the Integrability and Stability of Stationary Solutions of the Goryachev–Sretensky Gyrostat

On the Movement of Gyrostat under the Action of Potential and Gyroscopic Forces

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