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.     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: I

The problem of optimal control is considered for the motion of the center of mass of a spacecraft in a central Newtonian gravitational field. For solving the problem, two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems. Both the variants have a quaternion variable among the phase variables. In the first variant this variable characterizes the orientation of an instantaneous orbit of the spacecraft and (simultaneously) the spacecraft location in this orbit, while in the second variant only the instantaneous orbit orientation is specified by it. The suggested equations are convenient in the respect that they allow the general three-dimensional problem of optimal control by the motion of the spacecraft center of mass to be considered as a composition of two interrelated problems. In the first variant these problems are (1) the problem of control of the shape and size of the spacecraft orbit and (2) the problem of control of the orientation of a spacecraft orbit and the spacecraft location in this orbit. The second variant treats (1) the problem of control of the shape and size of the spacecraft orbit and the orbit location of the spacecraft and (2) the problem of control of the orientation of the spacecraft orbit. The use of quaternion variables makes this consideration most efficient. The problem of optimal control is solved on the basis of the maximum principle. Several first integrals of the systems of equations of the boundary value problems of the maximum principle are found. Transformations are suggested that reduce the dimensions of the systems of differential equations of boundary value problems (without complicating them). Geometrical interpretations are given to the transformations and first integrals. The relation of the vectorial first integral of one of the derived systems of equations (which is an analog of the well-known vectorial first integral of the studied problem of optimal control) with the found quaternion first integral is considered. In this paper, which is the first part of the work, we consider the models of motion of the spacecraft center of mass that employ quaternion variables. The problem of optimal control by the motion of the spacecraft center of mass is investigated on the basis of the first variant of equations of motion. An example of a numerical solution of the problem is given.     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: II

The problem of a rendezvous in the central Newtonian gravitational field is considered for a controlled spacecraft and an uncontrollable spacecraft moving along an elliptic Keplerian orbit. For solving the problem, two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems and using quaternion variables to describe the orientations of these coordinate systems. In the first variant of the equations of motion a quaternion variable characterizes the orientation of an instantaneous orbit of the spacecraft and the spacecraft location in the orbit, while in the second variant it characterizes the orientation of the plane of the spacecraft instantaneous orbit and the location of a generalized pericenter in the orbit. The quaternion variable used in the second variant of the equations of motion is a quaternion osculating element of the spacecraft orbit. The problem of a rendezvous of two spacecraft is formulated as a problem of optimal control by the motion of the center of mass of a controlled spacecraft with a movable right end of the trajectory, and it is solved on the basis of Pontryagin's maximum principle.     

Solving Optimization Problems for the Flight Trajectories of a Spacecraft with a High-Thrust Jet Engine in Pulse Formulation for an Arbitrary Gravitational Field in a Vacuum

A mathematically well-posed technique is suggested to obtain first-order necessary conditions of local optimality for the problems of optimization to be solved in a pulse formulation for flight trajectories of a spacecraft with a high-thrust jet engine (HTJE) in an arbitrary gravitational field in vacuum. The technique is based on the Lagrange principle of derestriction for conditional extremum problems in a function space. It allows one to formalize an algorithm of change from the problems of optimization to a boundary-value problem for a system of ordinary differential equations in the case of any optimization problem for which the pulse formulation makes sense. In this work, such a change is made for the case of optimizing the flight trajectories of a spacecraft with a HTJE when terminal and intermediate conditions (like equalities, inequalities, and the terminal functional of minimization) are taken in a general form. As an example of the application of the suggested technique, we consider in this work, within the framework of a bounded circular three-point problem in pulse formulation, the problem of constructing the flight trajectories of a spacecraft with a HTJE through one or several libration points (including the case of going through all libration points) of the Earth–Moon system. The spacecraft is launched from a circular orbit of an Earth's artificial satellite and, upon passing through a point (or points) of libration, returns to the initial orbit. The expenditure of mass (characteristic velocity) is minimized at a restricted time of transfer.     

One Class of Motions for a Satellite Carrying a Strong Magnet

The attitude motion of an artificial satellite carrying a strong magnet is studied. The approximate first integrals of the problem, i.e., adiabatic invariants, are indicated. The basic properties of the satellite motions close to the regular precessions with slowly varying parameters are established via the analysis of the adiabatic invariants.     

Structure of the Large-Scale Vortex Motions in the Ionosphere E Region

It is shown that the dissipative-centrifugal instability (DCI) revealed earlier for large-scale two-dimension vortex motions of the neutral gas in a fast-rotating atmosphere is also possible for similar motions of a weakly ionized gas in the magnetic field when one takes into account electrodynamics forces (the induction deceleration and gyroscopic force caused by the Hall current) in the absence of dissipation. In the case of a conductive atmosphere, strictly anticyclone motion at a DCI of the neutral atmosphere could be impossible or (depending on the Hall conductivity value) it could even change to a cyclone motion. Experimental results that can be considered as a confirmation of the theoretical conclusions are presented.     

Meteor wake in high frame-rate images--implications for the chemistry of ablated organic compounds

Extraterrestrial organic matter may have been chemically altered into forms more ameanable for prebiotic chemistry in the wake of a meteor after ablation. We measured the rate of cooling of the plasma in the meteor wake from the intensity decay just behind a meteoroid by freezing its motion in high frame-rate 1000 frames/s video images, with an intensified camera that has a short phosphor decay time. Though the resulting cooling rate was found to be lower than theoretically predicted, our calculations indicated that there would have been insufficient collisions to break apart large organic compounds before most reactive radicals and electrons were lost from the air plasma. Organic molecules delivered from space to the early Earth via meteors might therefore have survived in a chemically altered form. In addition, we discovered that relatively small meteoroids generated far-ultraviolet emission that is absorbed in the immediate environment of the meteoroid, which may chemically alter the atmosphere over a much larger region than previously recognized.     

Absolute IR-spectra from the measurement of Fourier-spectrometers aboard Meteor 25 and 28

It is well known that temperature- and watervapour-profiles, ozone concentration, other atmospheric constituents and the surface-radiation of the Earth can be determined by remote sensing in the IR radiation range with the aid of a satellite.

The narrow-band radiation measurements for remote sensing of the atmosphere and the Earth-surface can be realized either by various radiometers working in selected frequency channels or, continuously in a given frequency range, by spectrometers with fixed spectral resolution.

Fourier-spectrometers (FS) have been used in Earth-orbit only four times up to now: Nimbus 3, Nimbus 4, Meteor 25 and Meteor 28.

The most important technical parameters, the working regime and some aspects of date processing of the FSs working aboard of Meteor 25 and Meteor 28 are given. For the determination of calibrated absolute spectra a method is used that is based on the experience of the first experiment and on the long time stability of the spectrometers. The results obtained in laboratory calibration tests and in the orbit are described.     

Doppler Detection of Gravitational Bursts Using the Earth's Satellites

We discuss the possibility of detection of low-frequency gravitational waves by means of Doppler tracking of a relatively close satellite of the Earth. A detailed analysis is performed of electromagnetic fluctuations in the space communication channel and of the instrumental noise of receiving–transmitting systems. It is shown that when certain compensating procedures are used, one can detect gravitational radiation generated in star collapses and coalescences of binaries in our Galaxy in the frequency range from 2 × 10^–3 to 5 × 10^–1 Hz and with a metric variation amplitude of 10^–15 and higher.     

一种单路开环对消电路设计

文中设计一种形式新颖的开环对消电路 ,用于提高收发天线的隔离度 .它由耦合器、衰减器、移相电路和加法器组成。具有宽频带 ,结构简单 ,体积小等特点。试验结果表明 ,此对消电路可在 40 0 MHz工作频段内实现 1 0 d B以上对消比     

The Mode of Gravitational Orientation for the International Space Station

The results of the determination of the uncontrolled attitude motion of the International Space Station during its unmanned flight in 1999 are presented. The data of onboard measurements of three components of the angular velocity are used for this determination. These data covering an interval of slightly less than one orbit were jointly processed by the least squares method, by integrating the equations of motion of the station relative to its center of mass. As a result of this processing, the initial conditions of the motion and the parameters of the mathematical model used were estimated. The actual motion of the station has been determined for 20 such intervals during April–November. Throughout these intervals, the station rotated about the axis of the minimum moment of inertia, the latter executing small oscillations relative to the local vertical. Such a mode, known as the mode of gravitational orientation of a rotating satellite or the mode of generalized gravitational orientation, was planned before the flight. The measurements were made to verify it. The quasistatic component of the microaccelerations aboard the station is estimated for this mode.     

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.     

Resonance Effects when Moving a Small Spacecraft around the Center of Mass in a Deployable Tether System

Cosmic Research - The resonance motions of a small spacecraft relative to the center of mass when deploying a tether system are analyzed. The tether system is deployed from a base spacecraft moving...     

Gravitational maneuvers as a way to direct small asteroids to trajectory of a rendezvous with dangerous near-Earth objects

A possibility to prevent collisions with the Earth of dangerous celestial bodies by directing at them small asteroids is considered. It is proposed to solve this problem using a gravitational maneuver near the Earth.     

卫星光通信中耦合运动对光信号跟踪影响分析

光通信终端与卫星平台的耦合运动是影响卫星光通信系统光信号跟踪性能的重要因素。以铱星系统星间链路为例,建立了卫星光通信终端与卫星平台相互耦合运动的数学模型,并进行了数值仿真。理论分析及仿真结果表明:卫星光通信终端与卫星平台相互耦合运动使系统粗跟踪误差增大,方位轴、俯仰轴最大误差分别为94μrad和98μrad,超过精瞄系统补偿范围。为确保星间激光链路通信性能,提出了光束粗跟踪控制补偿算法,并进行了相应的仿真实验,仿真结果表明:补偿后的控制算法将方位轴、俯仰轴最大跟踪误差降低为37μrad和41μrad,符合精瞄系统补偿要求,保证了系统跟踪性能。该结果对今后小卫星星座激光组网具有一定的指导意义。     

激光陀螺误差建模与估计研究

首先用小波分解的方法对陀螺误差的趋势项进行了分析 ,采用Allan方差分析的方法 ,对某型激光陀螺误差进行了建模及误差估计研究 ,将激光陀螺误差中的零偏、量化噪声、及随机游走噪声等误差成分分离出来 ,并对其统计特性进行了估计。同时实验结果表明一阶马尔可夫噪声在激光陀螺误差中不占主要分量