On dynamics of a plasma ring rotating in the magnetic field of a central body: Magneto-gyroscopic waves. Problems of stability and quantization

Based on a mathematical model described in [1], some new aspects of the dynamics of a thin planar plasma ring rotating in the magnetic field of a central body are considered. The dipole field is considered assuming that the dipole has a small eccentricity, and the dipole axis is inclined at a small angle to the central body’s axis of rotation. Emphasis is placed on the problem of stability of the ring’s stationary rotation. Unlike [1], the disturbed motion is considered which has a character of eddy magneto-gyroscopic waves. The original mathematical model is reduced to a system of finite-difference equations whose asymptotic analytical solution is obtained. It is demonstrated that some “elite” rings characterized by integral quantum numbers are long-living, while “lethal” or unstable rings (antirings) are associated with half-integer quantum numbers. As a result, an evolutionally rife rotating ring of magnetized plasma turns out to be stratified into a large number of narrow elite rings separated by gaps whose positions correspond to antirings. The regions of possible existence of elite rings in near-central body space are considered. Quantum numbers determining elite eigenvalues of the mean sector velocity (normalized in a certain manner) of a ring coincide with the quantum numbers appearing in the solution to the Schrödinger equation for a hydrogen atom. Perturbations of elite orbits corresponding to these quantum numbers satisfy the de Brogli quantum-mechanical condition. This is one more illustration of the isomorphism of quantization in microcosm and macrocosm.     

Stability of a ring of connected satellites

The motion of a large number of artificial satellites connected in a ring one after another by tethers of variable length is considered. Every satellite is supposed to have a control system programmed according to some tether tension law as a function of the distance between tethered satellites. The effect of the tension control law on the stability of stationary rotation of this ring is investigated. The final stability condition includes two requirements: 1) the nominal tether tension should be less than a definite limit equal, up to numerical coefficient, to one satellite weight divided by the number of satellites; 2) tether tension should decrease (or remain constant) with the increase of the distance between tethered satellites. In dynamics the artificial rings of this kind are much like their natural prototype—meteor rings. On the other hand, the investigation of the artificial rings contributes to developing an unexpected view upon meteor rings, suggesting a model of an imaginary equivalent string.     

Planetary rings as relics of plasma pre-rings

A possibility is discussed that the rings of large planets observed in the modern epoch are relics of some pre-rings consisting of magnetized plasma (according to a hypothesis by H. Alfven). The solution to a model problem published in [36, 37] is used. Its main result is a mechanism of stratification of an evolutionally mature plasma pre-ring into a large number of narrow elite rings separated by anti-rings (gaps). Another result is the theoretical substantiation of the presence in the near-planetary space of a region of existence and stability (in what follows it is referred to as ES-region) of plasma rings. The data obtained in the course of the Voyager, Galileo, and Cassini missions are used below for verification of the model on which the solutions presented in [36, 37] are based.     

A hydrodynamic analogy of the solution to double-averaged Hill problem

A hydrodynamic analogy for the solution of doubly averaged Hill problem obtained by M.L. Lidov [1] is discussed. S.A. Chaplygin used a similar analogy reducing the two-dimensional problem of motion of a compressible fluid to the same problem for some fictitious incompressible fluid [2]. In this case, we are led to the range of ideas which go back to the work by N.E. Zhukowski [3]. Two versions of this hydrodynamic analogy, on the basis of the model of a stratified fluid (exact analogy) and on the basis of the model of a homogeneous fluid (approximate analogy), are considered as well as some consequences of them.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 2, 2005, pp. 126–134.Original Russian Text Copyright © 2005 by Rabinovich, Prokhorenko.     

改进的次时间最优控制

本文在[1][2]基础上进一步探讨了次时间最优控制的改进问题,深入地阐明了次时间最优控制的某些特性后,提出了一个新的改进的设计方法。按照这种方法设计控制系统,不但实用而且可以大幅度提高次时间最优控制的最优性。并用实例比较了各种方法,证明了本文提出的方法的优越性。本文提出的方法应用于工程设计,对于提高系统的最优性是非常有效的。     

Periodic motions of a nearly dynamically symmetric satellite in the neighborhood of hyperboloidal precession

The motion of a satellite close to a dynamically symmetric solid body in a Newtonian gravitational field over a circular orbit is studied. The system of differential equations describing the body’s motion is close to a system with cyclic coordinate. New classes of periodic motions are constructed in the neighborhood of a known partial solution to an unperturbed problem, hyperboloidal precession of a dynamically symmetric satellite. In the resonance case, when the ratio of one frequency of small oscillations of a reduced system with two degrees of freedom in the neighborhood of a stable equilibrium position to the frequency of cyclic coordinate variation is close to an integer number, there exist one or three families of periodic motions that are analytic in terms of fractional powers of a small parameter. A study of stability of these motions was performed with the help of KAM (Kolmogorov-Arnold-Moser) theoty. Faling the described resonance there exists a unique family of periodic motions that is analytic in terms of integer powers of a small parameter. The check-up of stability of these motrons was carried out. We distinguished the cases of parametric resonance, resonances of the third and fourth orders, and a non-resonant case. In the resonance cases our study relies on well-known results on stability of Hamiltonian systems during resonances [1]. In the non-resonant case we use the KAM theory [2].     

Super-elite plasma rings and the orbits of planets and satellites isomorphic to the orbits of electrons in the Bohr’s model of the hydrogen atom

This paper continues the series of papers [1–5] and generalizes the previous results to a proto-ring of magnetized plasma whose density decreases in the radial direction. The problem of quantization of the sector and orbital velocities, and of the radii and periods of revolution of elite plasma rings is considered. A new concept of super-elite rings is introduced. Their isomorphism with the orbits of the planets and planetary satellites in the Solar System is proved. This isomorphism also extends to the orbits of electrons in the Bohr’s model of the hydrogen atom.     

Gravitational and hydroelastic waves in thomson-delaney cells of the ocean on Jovian Moon Europa

The possibility of appearance of hydrothermal cells in the system “Ocean of Jovian Moon Europaits ice crust” was theoretically proved by R. Thomson and J. Delaney [8]. We formulated in [11] boundary value problems for planetary gyroscopic waves and gravitationally elastic waves in these cells, and the spectrum of nondivergent gyroscopic waves was numerically investigated. The present paper is a continuation of [11]. It considers the spectra of independent, purely gravitational and hydroelastic waves. The possibility of resonant excitation in Thomson-Delaney cells of gravitational and hydroelastic waves is considered.     

Comparative Analysis of Models of the Earth's Gravity: 3. Accuracy of Predicting EAS Motion

This paper continues a comparative analysis of modern satellite models of the Earth's gravity which we started in [6, 7]. In the cited works, the uniform norms of spherical functions were compared with their gradients for individual harmonics of the geopotential expansion [6] and the potential differences were compared with the gravitational accelerations obtained in various models of the Earth's gravity [7]. In practice, it is important to know how consistently the EAS motion is represented by various geopotential models. Unless otherwise stated, a model version in which the equations of motion are written using the classical Encke scheme and integrated together with the variation equations by the implicit one-step Everhart's algorithm [1] was used. When calculating coordinates and velocities on the integration step (at given instants of time), the approximate Everhart formula was employed.     

Controlling the motion of a spacecraft when approaching a large object of space debris

The problem of calculating the parameters of maneuvering a spacecraft as it approaches a large object of space debris (LOSD) in close near-circular noncoplanar orbits has been considered. In [1–4], the results of analyzing the problem of the flyby of the separated LOSD groups have been presented. It has been assumed that a collector spacecraft approaches the LOSD and captures it or it is inserted into the nozzle of a small spacecraft that has a proper propulsion system (PS). However, in these papers, the flight from one object to another was only analyzed and the problem of approaching to LOSD with a given accuracy was not considered. This paper is a supplement to the cycle of papers [1–4]. It is assumed that, the final stage of approaching the LOSD is implemented by maneuvering in many orbits (up to several dozens) with low-thrust engines, but the PS operating time is fairly small compared with the orbit period in order to make it possible to use impulse approximation in the calculations.     

RATAN-600 microwave observations of powerful active regions from October 23 to November 5, 2003

Application of the mode of azimuthal observations on RATAN-600 has made it possible to realize multiple daily observations [1]. The results of multiwavelength observations of the Sun in this mode point to the existence of sharp spectral irregularities in the polarized radiation of flare-productive active regions (FPARs) producing especially powerful flares [2]. These phenomena occur in a broad range of radio-emission fluxes (0.05–200 s.f.u.), in a rather narrow wavelength band (2–5 cm), and they are recorded during the time interval from several hours to several days before a powerful flare, as well as during the flare. Frequently, such events indicate an eruption of powerful coronal mass ejections and high-energy particle (proton) fluxes, which, when reaching the Earth’s magnetosphere, trigger its disturbances. Here, we analyze events in the microwave band connected with the strongest flares which took place on October 28 and November 4, 2003.     

A Modification of the Method of Transporting Trajectory

Further development of an approximate method for optimizing a flight with an ideally controlled small thrust is proposed. The method is based on the employment of the transporting trajectory and considered in [1–3]. A detailed analysis of the means of improving the accuracy of this method suggested in [2, 3] is carried out, and the solution is presented in finite form. The proposed approach is applied to the flights making flybys of many celestial bodies. In the case of small bodies the solution is also obtained in finite form. A numerical example is considered confirming the high efficiency of this method.     

同轴线的时域并矢格林函数及特性分析

本文利用Ohm-Rayleigh法导出了同轴线的时域并矢格林函数,并修正了[1]的错误。同时也指出了[2]在修正[1]时的不足。文中还讨论了理想探针激励下同轴线的瞬变特性,分析了高次模的时域波形性质。这对进一步分析同轴线在时域中工作的特点有一定的指导意义。     

Deformation of the Envelope of a Broadband Signal during Propagation through the Martian Ionosphere

The regularities of propagation along the spacecraft-Martian surface-spacecraft path of a broadband Gaussian pulse in the condition of its dispersion distortions are considered in application to the problem of radiowave pulse sounding of the near-surface soil of Mars from onboard a satellite. The Martian night-side ionosphere reduces the energy considerably but does not lead to any distortion of the pulse envelope. At the sounding of a two-layer surface, the ionosphere influence, together with the signal absorption, manifests as the lower limit of the thickness of the upper layer reached for measurements in the scope of the planned experiment [1].     

对遥控系统误指令概率计算近似公式的推敲

在关于遥控指令错误概率的讨论中 ,提出了一些误指令概率近似计算公式 ,文中对此做了进一步的推敲 ,在概念上作了清理 ,分析它们各自可能产生误差的原因 ,并用实例比较它们的大小。最后也提出一种近似计算公式建议     

Synthesis of a combined system for precise stabilization of the Spektr-UF observatory: II

The paper presents the second part of the results of search studies for the development of a combined system of high-precision stabilization of the optical telescope for the designed Spectr-UF international observatory [1]. A new modification of the strict method of the synthesis of nonlinear discrete-continuous stabilization systems with uncertainties is described, which is based on the minimization of the guaranteed accuracy estimate calculated using vector Lyapunov functions. Using this method, the synthesis of the feedback parameters in the mode of precise inertial stabilization of the optical telescope axis is performed taking the design nonrigidity, quantization of signals over time and level, and errors of orientation meters, as well as the errors and limitation of control moments of executive engine-flywheels into account. The results of numerical experiments that demonstrate the quality of the synthesized system are presented.     

主成分估计的发展和完善及其在制导工具误差分离中的应用

本丈针对制导工具误差模型的特点,对[4]的主成分估计法作了深入的理论研究,发展和完善了[4]的方法,得到了一种适用于制导工具误差系数分离的方法。     

细长飞行器的气动弹性发散分析

本文从下列两方面推广文献[1]中的二升力火箭弹体气动弹性发散分析:一是把两个集中升力扩大到任意个集中升力;二是计及空气动力干扰效应。