The Set of Relative Equilibria of a Stationary Orbital Asymmetric Gyrostat

被引：0

作者：

Chaikin S.V. ^{[1
]}

机构：

[1] Matrosov Institute of System Dynamics and Control Theory, ul. Lermontova 134, Irkutsk

来源：

Journal of Applied and Industrial Mathematics | 2019年 / 13卷 / 1期

基金：

俄罗斯基础研究基金会;

关键词：

central Newtonian field of attraction forces; circular orbit; orbital gyrostat; relative equilibria; structure of the set of equilibria;

D O I：

10.1134/S1990478919010046

中图分类号：

学科分类号：

摘要：

Under consideration is the well-known problem of relative equilibria (an equilibrium position in the orbital coordinate system) of a gyrostat satellite and their dependence on the design parameters. A new geometric approach to the analysis of the set of relative equilibria is developed. It is proposed to determine the relative equilibria in the corresponding three-dimensional Euclidean space using special aggregated parameters of the systemby the coordinates of the intersection points of two pairs of corresponding hyperbolic cylinders with the sphere of the unit radius. It is shown that, for arbitrary values of the gyrostatic moment and other parameters of the system, there are at least eight different relative equilibria. © 2019, Pleiades Publishing, Ltd.

引用

页码：30 / 35

页数：5

共 11 条

[1]

Beletskii V.V., Motion of an Artificial Satellite Relative to the Center of Mass, (1965)

[2]

Beletskii V.V., Chaikin S.V., Allowance for the Displacement of the Center of Mass of a Gyrostat with an Elastic Beam in the Analysis of the Stability of a Family of Its Equilibria, Vestnik Moskov. Gos. Univ. Ser. 1,Mat.Mekh., 1, pp. 42-47, (2006)

[3]

Chaikin S.V., Uniaxial Equilibrium Orientations Toward the Attracting Center of a Symmetrical Prolate Orbital Gyrostat with an Elastic Rod, Sibir. Zh. Industr.Mat., 20, 3, pp. 92-100, (2017)

[4]

Stepanov S.Y., On a Set of Motions of a Satellite-Gyrostat in a Central Newtonian Field of Forces and Stability ofMotions, Prikl. Mat. iMekh., 33, 4, pp. 737-744, (1969)

[5]

Chaikin S.V., Relative Equilibria of a Gyrostat on a Circular Orbit under Small Going of the Gyrostatic Moment out of ItsMain Central Plane of Inertia, 9th All-Russian Congress on Theoretical and Applied Mechanics. Abstracts, Vol. 1, (2006)

[6]

Anchev A.A., On Stabilization of Relative Equilibrium of a Satellite with Flywheels, Kosmich. Issled., 4, 12, pp. 192-202, (1966)

[7]

Roberson R.E., Hooker W.W., Gravitational Equilibria of Rigid Body Containing Symmetric Rotors, Proceedings of 17th Congress Internat. Astronaut. Madrid, 1966, (1967)

[8]

Rubanovskii V.N., On Bifurcation and Stability of Relative Equilibria of a Satellite-Gyrostat, Prikl. Mat. i Mekh., 55, 4, pp. 565-571, (1991)

[9]

Sarychev V.A., Gutnik S.A., To a Question on Relative Equilibrium Position of a Satellite-Gyrostat, Kosmich. Issled., 22, 3, pp. 323-326, (1984)

[10]

Horn R.A., Johnson C.R., Matrix Analysis, (1985)

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