Dynamics of a gyrostat satellite with the vector of gyrostatic moment in the principal plane of inertia

Dynamics of a gyrostat satellite moving along a circular orbit in a central Newtonian field of force is investigated. In a particular case, when the gyrostatic moment vector lies in one of the satellite’s principal central planes of inertia, all positions of equilibrium are determined, and the conditions of their existence are analyzed. Also determined are bifurcation values of dimensionless parameters, at which the number of equilibrium positions changes. As a result of analysis of the generalized energy integral, for each equilibrium orientation the sufficient conditions of stability are derived. Evolution of the regions where the sufficient conditions of stability are valid is investigated under variation of the system’s dimensionless parameters.     

Satellite dynamics under the influence of gravitational and aerodynamic torques. A study of stability of equilibrium positions

The dynamics of the rotational motion of a satellite, moving in the central Newtonian force field under the influence of gravitational and aerodynamic torques, is investigated. The paper proposes a method for determining all equilibrium positions (equilibrium orientations) of a satellite in the orbital coordinate system for specified values of aerodynamic torque and the major central moments of inertia; the sufficient conditions for their existence are obtained. For each equilibrium orientation the sufficient stability conditions are obtained using the generalized energy integral as the Lyapunov function. The detailed numerical analysis of the regions where the stability conditions of the equilibrium positions are satisfied is carried out depending on four dimensionless parameters of the problem. It is shown that, in the general case, the number of satellite’s equilibrium positions, for which the sufficient stability conditions are satisfied, varies from 4 to 2 with an increase in the value of the aerodynamic torque magnitude.     

Gravity-oriented satellite dynamics subject to gravitational and active damping torques

The dynamics of the rotational motion of a satellite moving in the central Newtonian field of force over a circular orbit under the effect of gravitational and active damping torques, which depend on the satellite angular velocity projections, has been investigated. The paper proposes a method of determining all equilibrium positions (equilibrium orientations) of a satellite in the orbital coordinate system for specified values of damping coefficients and principal central moments of inertia. The conditions of their existence have been obtained. For a zero equilibrium position where the axes of the satellite-centered coordinate system coincide with the axes of the orbital coordinate system, the necessary and sufficient conditions for asymptotic stability are obtained using the Routh–Hurwitz criterion. A detailed analysis of the regions where the conditions of the asymptotic stability of a zero equilibrium position are fulfilled have been obtained depending on three dimensionless parameters of the problem, and the numerical study of the process of attenuation of satellite’s spatial oscillations for various damping coefficients has been carried out. It has been shown that there is a wide range of damping parameters from which, by choosing the necessary values, one can provide the asymptotic stability of satellite’s zero equilibrium position in the orbital coordinate system.     

Optimum parameters of a gravitational satellite-stabilizer system

Dynamics of a satellite-stabilizer system is studied. It is supposed that there is a viscous friction in a hinge connecting two bodies, but there is no elasticity. The attitude motion in a plane of circular orbit is considered, and parameters are determined, at which natural oscillations near a stable equilibrium position in the orbital coordinate system are damped out most rapidly. The rate of transient processes is estimated by a value of the degree of stability of linearized equations of motion. The optimization of the degree of stability is sequentially performed in dimensionless damping coefficient (the first stage) and in inertial system parameters (the second stage). The result of the first stage is the partition of system parameter space into the regions, in each of which the maximum of the degree of stability is reached on a particular configuration of roots of the characteristic equation. It is shown at the second stage that the global maximum is reached at two points of parameter space, where one of system bodies degenerates into a plate, and the characteristic equation has four equal real roots.     

Equilibrium attitude and stability of a spacecraft on a stationary orbit around an asteroid

The stationary orbits around an asteroid, if exist, can be used for communication and navigation purposes just as around the Earth. The equilibrium attitude and stability of a rigid spacecraft on a stationary orbit around a uniformly-rotating asteroid are studied. The linearized equations of attitude motion are obtained under the small motion assumption. Then, the equilibrium attitude is determined in both cases of a general and a symmetrical spacecraft. Due to the higher-order inertia integrals of the spacecraft, the equilibrium attitude is slightly away from zero Euler angles. Then necessary conditions of stability of this conservative system are analyzed based on the linearized equations of motion. The effects of different parameters, including the harmonic coefficients C₂₀ and C₂₂ of the asteroid and higher-order inertia integrals of the spacecraft, on the stability are assessed and compared. Due to the significantly non-spherical shape and rapid rotation of the asteroid, the effects of the harmonic coefficients C₂₀ and C₂₂ are very significant, while effects of the third- and fourth-order inertia integrals of the spacecraft can be neglected. Considering a spacecraft on a stationary orbit around an example asteroid, we show that the classical stability domain predicted by the Beletskii–DeBra–Delp method on a circular orbit in a central gravity field is modified due to the non-spherical mass distribution of the asteroid. Our results are confirmed by a numerical simulation.     

Stability of triangle libration points in generalized restricted circular three-body problem

Equilibrium positions of a small-mass body are considered with respect to a precessing dumbbell. The dumbbell represents two rigidly fixed spherical gravitating bodies. Such a system can be considered as a model of a binary asteroid. Stability of relative equilibrium positions with equal distances from the small mass to the attracting centers is studied. By analogy with the classical restricted three-body problem, these positions are referred to as triangle libration points. It is shown that the character of stability of these libration points is determined by three constant parameters: nutation angle and angular velocity of precession, as well as the ratio of masses at the ends of the dumbbell. Stability conditions are derived in the linear approximation, and the regions of stability and instability in the space of problem parameters are constructed. The paper is a continuation of [1].     

Stability and chaos of a damped satellite partially filled with liquid

The stability and chaotic motions of a damped satellite partially filled with liquid which is subjected to external disturbance are investigated in this paper. With linearization analysis, the stability of the two non-trivial equilibrium points is studied. The homoclinic and heteroclinic orbits are found by using the undetermined coefficient method, and the convergence of the series expansions of these two types of orbits is proved. It analytically demonstrates that there exist homoclinic orbits of the Si’lnikov type that join the two non-trivial equilibrium points to themselves, and therefore smale horseshoes and the horseshoe chaos occur for this system via the Si’lnikov criterion. In addition, there also exists a heteroclinic orbit connecting the two non-trivial equilibrium points. Numerical simulations are also given, which verify the analytical results. The system can be chaotic through period-doubling bifurcations as the amplitude of the external disturbance varies, and backward period-doubling bifurcations as the angular momentum of the rotor varies.     

Dynamics of an axisymmetric gyrostat satellite under the action of gravitational moment

Dynamics of an axisymmetric gyrostat satellite moving in the central Newtonian force field along a circular orbit is investigated. All equilibrium positions of the gyrostat satellite in the orbital coordinate system are determined, and the sufficient stability conditions of equilibrium positions are derived.     

Evolution of the Motion of a Viscoelastic Sphere in a Central Newtonian Field

The evolution of translational-rotational motion of a viscoelastic sphere in a central Newtonian field is studied. By the method of separating motions and averaging in the generalized Andoyer–Delaunay variables, equations are derived that describe the evolution of motion. The analysis of the approximate equations obtained is performed. The condition of existence of a steady-state motion is found, and its stability is investigated using the equations in variations.     

一种用于垂直降落重复使用运载器的缓冲器性能分析

以对称分布四腿支柱式垂直降落重复使用运载器为研究对象,基于一种新型油液-蜂窝式多级缓冲器,建立了计及地面弹塑性变形的运载器软着陆过程动力学模型,并给出了运载器着陆时的五种临界着陆工况。以前四种着陆工况为基础对多级缓冲器进行了缓冲参数协调分析,在此基础上以翻倒极限着陆工况为基础重点研究了多级缓冲器缓冲参数对着陆稳定性能的影响。研究表明多级缓冲器中油孔面积、活塞杆直径和阻尼阀调节弹簧预紧力等油液缓冲参数对蜂窝压溃载荷的选取有着显著影响,同时以上参数的合理选择可以有效增加运载器的着陆稳定性能。     

Gravitationally Perturbed Elastic Waves in the Hidden Ocean of Europa

The frequency spectrum of joint hydro-elastic vibrations of the ice surface of the ocean and liquid is analyzed taking into account the proper gravity field of Europa, one of Jupiter’s moons. It is shown how the methods developed for analysis of the vibration stability of earth buildings are used to study seismic properties of the natural Jupiter satellite Europa. Numerical estimates show that when studying the electromagnetic effects and seismic properties of this satellite one should take into account hydro-elastic characteristics due to the closeness of the corresponding frequency spectra.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 3, 2005, pp. 209–214.Original Russian Text Copyright © 2005 by Dokuchaev.     

Estimation of the Probability of Radiation Failures and Single Particle Upsets of Integrated Microcircuits onboard the <Emphasis Type="Italic">Fobos-Grunt</Emphasis> Spacecraft

When designing the radio-electronic equipment for long-term operation in a space environment, one of the most important problems is a correct estimation of radiation stability of its electric and radio components (ERC) against radiation-stimulated doze failures and one-particle effects (upsets). These problems are solved in this paper for the integrated microcircuits (IMC) of various types that are to be installed onboard the Fobos-Grunt spacecraft designed at the Federal State Unitary Enterprise “Lavochkin Research and Production Association.” The launching of this spacecraft is planned for 2009.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 3, 2005, pp. 237–239.Original Russian Text Copyright © 2005 by Kuznetsov, Popov, Khamidullina.     

Power Losses of Solar Arrays under the Action of an Environment in a Geosynchronous Orbit

We derive calculated and experimental relations characterizing the reduction in the electric power of solar arrays under prolonged (∼10 years) action of the environment in orbit. The influence of separate factors related to the environment on the loss of solar arrays power is studied. The following factors are considered: ionizing and ultraviolet emissions, contamination of protective glass by the products of destruction of the outer surface materials of spacecraft, thermal cycling, radiation electrization, and plasma thrusters plumes.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 4, 2005, pp. 274–282.Original Russian Text Copyright © 2005 by Shuvalov, Kochubei, Gubin, Tokmak.     

Autogeneration of an Instability of a Plasma Composition Equilibrium in the Plasmaspheric Transition Region during a Postsunset High-Altitude Launch of the Vertikal'-10 Rocket

A cause of the instability of equilibrium of plasma ion composition is discussed and exemplified by the data on a burst of amplitudes of small-scale plasma irregularities in the plasmaspheric transition region during an evening launch of the Vertikal'-10 rocket. This burst is accompanied by a simultaneous decrease in the average plasma density at altitudes of 700–1100 km. Specific features of the observed events are compared to postsunset incoherent scatter radar observations of the ion diffusion flux density. It is demonstrated that the instability is caused by peculiarities of the protonosphere–ionosphere interaction associated with a sharp difference between thermal conditions of the ionospheric and protonospheric air shortly after sunset. The induced nonuniformity of postsunset cooling of the protonospheric–ionospheric plasma causes density irregularities in ion diffusion fluxes and generates local bunches of heavy ions, which are usually only a minor impurity to lighter ions. As a result, conditions are created that are favorable for the nondissipative accumulation of potential energy for the mutual opposition of two or more groups of ions with different masses and for the subsequent release of this energy by a threshold excitation of impurity-driven plasma instabilities.     

Internal Gravitational Field of a Thin Homogeneous Ring

The potential of gravity forces is found inside a thin homogeneous ring when the ring’s mean radius is much larger than the diameter of its cross section. Rings with elliptic and almost circular cross sections are considered.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 4, 2005, pp. 260–268.Original Russian Text Copyright © 2005 by Kasatkin.     

A Study of Oscillations near a Resonance during the Descent of a Spacecraft in the Atmosphere

An analysis of the stability of the resonance motion of a spacecraft with a small asymmetry during its descent in the atmosphere is carried out. In the vicinity of the main resonance, the action–angle variables are introduced and an equation of the variation of action is composed. A conclusion related to the stability of the resonance motion is made from the investigation of this equation. Sufficient conditions of stability of the resonance motion of a spacecraft are obtained and represented in a form convenient for analysis.     

Stability and chaos of a damped satellite partially filled with liquid

The stability and chaotic motions of a damped satellite partially filled with liquid which is subjected to external disturbance are investigated in this paper. With linearization analysis, the stability of the two non-trivial equilibrium points is studied. The homoclinic and heteroclinic orbits are found by using the undetermined coefficient method, and the convergence of the series expansions of these two types of orbits is proved. It analytically demonstrates that there exist homoclinic orbits of the Si’lnikov type that join the two non-trivial equilibrium points to themselves, and therefore smale horseshoes and the horseshoe chaos occur for this system via the Si’lnikov criterion. In addition, there also exists a heteroclinic orbit connecting the two non-trivial equilibrium points. Numerical simulations are also given, which verify the analytical results. The system can be chaotic through period-doubling bifurcations as the amplitude of the external disturbance varies, and backward period-doubling bifurcations as the angular momentum of the rotor varies.     

Dynamics of an axisymmetric satellite under the action of gravitational and aerodynamic torques

Dynamics of attitude motion of an axisymmetric satellite moving in a circular orbit under the action of gravitational and aerodynamic torques is investigated. All equilibrium positions of the satellite in the orbital coordinate system are determined numerically, and sufficient conditions of stability of the equilibrium positions are derived.     

Neutralization of negative electric charge of a satellite by ionospheric plasma ions

The dynamics of the process of neutralization of a satellites negative electric charge by the charge of a layer of positive ions of ionospheric plasma is investigated. The changes in the electric field strength, as well as in the velocity and density of plasma ions, are obtained depending on the initial position of a particle and the distance to the satellites surface. It is found that under the conditions of accepted approximations, as the time grows unlimitedly, the satellites charge tends to zero but does not reach this value. The time during which the satellites electric charge decreases in magnitude as many times as specified is determined. It is shown that the negative charge of a satellite and the charge of a layer of plasma ions can form a structure of a double charged layer type whose lifetime is much longer than the time of its formation.Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 1, 2005, pp. 9–18.Original Russian Text Copyright © 2005 by Fedorov.