Mathematical models of high temperature flow in gas ducts of rocket engines

Results are given on certain dynamic properties of a high temperature and pressure gas flow. The investigation concerns the effect of sonic processes on the transfer of external signals by the flow and of the gas nonidealities on the properties of a linear and a nonlinear mathematical model of the jet nozzle. The investigation was conducted by the method of small parameters for differential equations of the dynamics of the gas flow, with the help of invariants of these equations, and estimates of solutions with arbitrary signals of a specific class. The results lead to estimates of errors due to usual simplifications of gas flow models such as linearization of jet nozzle equations and neglect of sonic processes. The errors of the latter kind are shown to depend on the Mach number and smoothness of signals. Accurate and approximate models of nozzle flow are obtained useful for controllability analysis of rocket engines. Some computation examples are given.     

Capabilities to Control the Throw-Weight of Ballistic Missiles by the Mobile Radar Data

The methods of estimating the throw-weight of ballistic missiles are analyzed on the basis of radar observations of different phases of BM trajectory from the instant of launch to the instant of impact of detachable elements. Approximate estimations of the accuracy of resulting estimations of mass, which are achieved by modern radars obtaining the data from three main phases of the BM trajectory, are given.     

Analysis of the Accuracy of Ballistic Descent from a Circular Circumterrestrial Orbit

The problem of the transportation of the results of experiments and observations to Earth every so often appears in space research. Its simplest and low-cost solution is the employment of a small ballistic reentry spacecraft. Such a spacecraft has no system of control of the descent trajectory in the atmosphere. This can result in a large spread of landing points, which make it difficult to search for the spacecraft and very often a safe landing. In this work, a choice of a compromise scheme of the flight is considered, which includes the optimum braking maneuver, adequate conditions of the entry into the atmosphere with limited heating and overload, and also the possibility of landing within the limits of a circle with a radius of 12.5 km. The following disturbing factors were taken into account in the analysis of the accuracy of landing: the errors of the braking impulse execution, the variations of the atmosphere density and the wind, the error of the specification of the ballistic coefficient of the reentry spacecraft, and a displacement of its center of mass from the symmetry axis. It is demonstrated that the optimum maneuver assures the maximum absolute value of the reentry angle and the insensitivity of the trajectory of descent with respect to small errors of orientation of the braking engine in the plane of the orbit. It is also demonstrated that the possible error of the landing point due to the error of specification of the ballistic coefficient does not depend (in the linear approximation) upon its value and depends only upon the reentry angle and the accuracy of specification of this coefficient. A guided parachute with an aerodynamic efficiency of about two should be used at the last leg of the reentry trajectory. This will allow one to land in a prescribed range and to produce adequate conditions for the interception of the reentry spacecraft by a helicopter in order to prevent a rough landing.     

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.     

时间、空间及运动的测量原理与时间和空间的理论

本文从分析时间、空间及运动的测量机理出发建立的时间和空间理论。导出了建立在电磁信号单向传递的相对性原理基础上的时空对称的新加里略变换，并证明了麦克斯韦方程对新加里略变换的协变性。阐明了光速不变原理和洛伦兹变换的物理意义和实质。引进了两套自治的速度定义，对应两套自治的变换。讨论了超光速运动的测量机制，相对运动特征出现负值是超光速运动的特征，导出了对应超光速运动的新加里略变换和洛伦兹变换。     

Thermal fatigue in structural components of flying vehicles engines

The paper deals with the problems of deformation and damage of the materials of structural components of complex shape subjected to cyclic loading by convective thermal flows which induces in them non-uniform temperature and thermal-stress fields. A new testing technique is proposed employing the use of models of different shape and, in particular, those of wedge-shape prism type. Variation of the level of thermal stresses and temperatures, as well as of the degree of non-uniformity of temperature and stress fields, is effected by changing the models dimensions under the given thermal loading conditions. It is shown that in simultaneous testing of a great number of models of different size it is possible to obtain information sufficient for deriving the equations of the material state under complex thermo-mechanical loading in aggressive gas flows. Examples are presented of practical application of the technique proposed.     

AP粒度和包覆层对硼燃烧的影响

通过对AP和硼及其混合物进行热分析实验,研究了硼在AP分解过程中参与反应的程度;用氧弹式量热计测试含硼富燃料推进剂的爆热,分析硼在推进剂燃烧过程中的放热。结果表明,对各组分含量相同的含硼富燃料推进剂用AP包覆硼粒子和提高超细AP含量可促使硼在AP分解过程中参与反应,使AP／B(1：1)热分解的放热量增加,提高推进剂的爆热,有利于推进剂中硼的燃烧。     

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.     

Optimization of the Flight of a Spacecraft with a Solar Sail from the Earth to Mars with a Perturbation Maneuver near Venus

The trajectories of the fastest flight of a spacecraft (SC) with a solar sail from the Earth's sphere of activity to the Martian sphere of activity including the section of a perturbation maneuver near Venus are investigated. The planetary spheres of activity are assumed to be point-like; i.e., the maneuver section and the initial and final positions of the SC coincide with the corresponding positions of the planets. The initial velocity of the SC is assumed to be equal to the Earth's velocity, so that no leveling of the velocities of the SC and Mars in the final point of the flight is required. The perturbation maneuver is considered as a jump of the heliocentric velocity of the SC at the point of its contact with Venus, which does not change the magnitude of its Venus-centric velocity. The orbits of planets are assumed to be circular and coplanar; the SC trajectory lies at the plane of these orbits. The sail is planar with a specularly reflecting surface. The trajectories of optimum flights are determined as a result of solving the boundary value problem of the Pontryagin maximum principle. The families of solutions to this problem depending on the initial angular positions of Venus and Mars are constructed by the method of continuation over a parameter.     

Estimate of accuracy of determining the orientation of the star sensor system according to the experimental data

The BOKZ-M60 star sensor (Unit for Measuring Star Coordinates) is intended for determining the parameters of the orientation of the axes of the intrinsic coordinate system relative to the axes of the inertial system by observations of the regions of the stellar sky. It is convenient to characterize an error of the single determination of the orientation of the intrinsic coordinate system of the sensor by the vector of an infinitesimal turn of this system relative to its found position. Full-scale ground-based tests have shown that, for a resting sensor the root-mean-square values of the components of this vector along the axes of the intrinsic coordinate system lying in the plane of the sensor CCD matrix are less than 2″ and the component along the axis perpendicular to the matrix plane is characterized by the root-mean-square value of 15″. The joint processing of one-stage readings of several sensors installed on the same platform allows us to improve the indicated accuracy characteristics. In this paper, estimates of the accuracy of systems from BOKZ-M60 with two and four sensors performed from measurements carried out during the normal operation of these sensors on the Resurs-P satellite are given. Processing the measurements of the sensor system allowed us to increase the accuracy of determining the each of their orientations and to study random and systematic errors in these measurements.     

Effect of orientation of the solar wind magnetic clouds on the seasonal variation of geomagnetic activity

An analysis is made of the causes of seasonal dependence of geomagnetic activity, taking into account orientation of large-scale plasma structures (of the magnetic cloud type) of the solar wind. The contribution of magnetic clouds of different orientation in the periods of equinoxes and solstices is demonstrated. It is established that in equinox periods the geomagnetic activity increases due to ejections with small angles of inclination of their axis to the ecliptic plane, most frequently detected in near-Earth space. In solstice periods, such clouds are not geoeffective structures because of a decreased magnitude of projection of the magnetic field of cloud axis onto the Earth’s magnetic dipole during such intervals. This effect reveals itself in a reduced level of geomagnetic activity in summer and winter.     

Computer search of variants for vehicle system composition synthesis

The design experience of vehicles systems composition synthesis is summerized. Some engineering techniques are suggested, which give an opportunity to solve the problems of a composition synthesis by means of a computer. These techniques are based on the following principles: construction of statistical models for the analysis of criteria behaviour; using of methods of the theory of extreme values statistics for the evaluation of the criteria limiting values; deriving of suboptimum variants groups; using of heuristic procedures for a cyclic correction of the search process in order to specify the range of boundary solutions for the problems with several criteria; using of a probabilistic appraisal for an estimation of search results; construction of educating algorithms using a fine for the variable values (composition variants); clearing up in the course of a dialogue process the interaction of an engineer with a computer.As in the design practice no requirements are extended to the algorithms of vehicle system characteristics design, that is why it is not possible at the stage of design solutions search to use the known recommendations worked out for the problems of linear, non-linear and dynamic programming.     

Architectural design for space tourism

The paper describes the main issues for the design of an appropriately planned habitat for tourists in space.Due study and analysis of the environment of space stations (ISS, MIR, Skylab) delineate positive and negative aspects of architectonical design. Analysis of the features of architectonical design for touristic needs and verification of suitability with design for space habitat.Space tourism environment must offer a high degree of comfort and suggest correct behavior of the tourists. This is intended for the single person as well as for the group. Two main aspects of architectural planning will be needed: the design of the private sphere and the design of the public sphere.To define the appearance of environment there should be paid attention to some main elements like the materiality of surfaces used; the main shapes of areas and the degree of flexibility and adaptability of the environment to specific needs.     

复合材料层合板热-力作用下的失效研究

碳纤维复合材料力学性能优异,在航空航天等领域广泛使用,其在热-力联合作用下的损伤失效研究对于结构的损伤破坏和强度预测具有重要意义。发展了热力耦合条件下复合材料结构渐进损伤分析方法,建立了三维有限元热烧蚀模型,并验证了计算模型的可靠性;采用三维Hashin失效准则,结合材料刚度突然退化模式,建立了失效分析模型,仿真分析了热-力联合作用下复合材料层合板损伤演化全过程。结果表明,该方法不仅能够较好地模拟复合材料层合板从局部失效的萌生、扩展直至结构完全失效的全过程,而且可以直观地显示结构的损伤失效模式,预测结构在不同条件下的承载能力。     

空间机械臂关节动力学建模与分析的研究进展

空间机械臂的机械部分是一个由关节和臂杆等结构、机构部件组成,在空间零重力环境下运行的多体系统。关节是空间机械臂的核心部件,在机械臂动力学特性中起着重要的作用。准确全面地了解关节的动力学特性,是正确分析与模拟机械臂系统空间运动特性的关键,而建立精确的关节动力学模型,是机械臂系统设计、分析和控制的基础。文章结合空间应用的特殊性,对机械臂关节动力学建模方法的发展过程和研究成果进行了总结;并讨论了关节模型的求解算法;最后,对空间机械臂关节动力学建模与分析方面有待进一步研究的问题进行了展望。     

Multipole Models of the Earth's Magnetic Field

To develop a mathematical model of rotational motion of an artificial satellite about its center of mass under the action of various forces (magnetic, Lorentz, etc.) caused by the geomagnetic field, it is necessary to know the induction of the Earth's magnetic field (EMF) as a function of the radius vector of a given point in the near-Earth space. Because the EMF possesses a complex structure and the above-mentioned functional dependence is unavailable in explicit analytic form, a set of approximate models of the EMF should be used. The simplest such model—a right dipole (aligned with the axis of rotation)—does not enable one to reveal in detail the influence of diurnal EMF rotation on the rotational motion of a satellite. The next EMF approximation—an inclined magnetic dipole—does not suffer from the above-mentioned drawback. However, it is shown that not all corrections to the magnetic induction of the EMF of the same order of magnitude are taken into account in the course of transformation from the model of aligned dipole to the model of inclined dipole. So, to develop the EMF model accurately accounting for the absence of axial symmetry of the EMF with respect to the axis of diurnal rotation of the Earth, in general, the effect of the quadrupole component of the geomagnetic potential on the EMF induction (and, probably, even the components of higher orders) must be taken into consideration. By using the International Geomagnetic Reference Field IGRF-2000, the multipole models of the EMF, corresponding to quadrupole, octupole, and higher-order approximations, were constructed and studied in this work. The EMF potential is expressed in terms of its multipole tensors. As a result, projections of the induction and induction gradient of EMF in the center of mass of the satellite onto the axes of the orbital coordinate system can be written in convenient and concise form. The expressions for the first four multipole tensors through the known geomagnetic constants are found. A method for estimating the reliability of these models is put forward, and the regions of applicability of the quadrupole and octupole models are drawn on the plane of orbital parameters.     

Spectrum of Natural Vibrations of the Ice Ocean of Jupiter's Moon Europa

The hydroelastic vibrations of the ice surface of the ocean of Europa, a natural satellite of Jupiter, are investigated, and the natural spectrum of frequencies of this surface is determined. The mathematical model of the mechanical system under consideration is presented in the form of a spherical shell, which is wetted by a spherical layer of liquid enveloping a rigid spherical core. The solution of the boundary value problems of the theory of elasticity is sought in the form of expansions into series of the associated Legendre polynomials. It is noted that there are at least three tones of natural vibrations of the shell–spherical liquid layer system, whose periods lie in the vicinity of the ten-hour period of Jupiter's rotation about its axis, and variations of the magnetic field of Europa with the same period.     

Impact of helio-and geophysical disturbances on thermobaric and climatic characteristics of the Earth’s troposphere

We present the mechanism and the concept of a model of the solar activity impact on thermobaric and climatic characteristics of the troposphere. Both are based on the idea of parametric action. The results of analysis are presented concerning specific features and regularities of changes in temperature regime of the troposphere in the period of variable helio-and geophysical activity, as well as long-term variations of temperature and heat content of the troposphere. The influence of changes in circulation in the atmosphere and ocean on processes in the system atmosphere-ocean-cryosphere is considered: thermohaline circulation of the oceans and energy exchange between the atmosphere and ocean. The revealed regularities find their complete explanation within the context of a model and mechanism of solar activity impact on climatic characteristics of the troposphere that were suggested previously by the authors.