突扩后缩型喷管前腔的流场计算

本文是为解决有关发动机喷管的实际烧蚀问题而进行的喷管前腔流场计算分析的一部分。探讨了SIMPLE算法在复杂边界下运行问题,重点研究了突扩后缩型喷管前腔的流场结构。计算表明:本文所提供的双涡系统与Finaish等人的结论是一致的,进一步证实了F.Pan和A.Acrivos的嵌套涡族理论。     

Generalized problem of two fixed centers

In the problem under consideration, the libration points are determined, and their stability is investigated. The surfaces of zero velocity are constructed, and the regions where motion is possible are found. The limiting case of the problem is considered.     

Theory of type III radio bursts in the interplanetary space: I. Derivation of permittivity tensor for the system consisting of electron beam and solar wind plasma

The tensor of permittivity for the system “electron beam - plasma of the interplanetary space” is derived in the approximation of geometrical optics. The problem is one-dimensional; all parameters such as density of the beam and of the solar wind plasma, and the induction of the interplanetary magnetic field are assumed to be dependent only on the distance to the Sun. The beam is generated by an active region during a solar flare, and it is a source of radio bursts of type III in the interplanetary space. The tensor of permittivity was obtained to close field equations by a material equation. On the basis of these equations it becomes possible to study theoretically the amplitude-frequency characteristics of the radio bursts as disturbances of the above-described beam-plasma system.     

About one problem of trajectory optimization

The optimization problem for trajectories of spacecraft flight from the Earth to an asteroid is considered in this paper. The flight is realized in the central Newtonian gravitational field of the Sun with a possibility of gravitational maneuvers near planets. Perturbation maneuvers are taken into account using the method of point area of action with a limitation on the flyby altitude. The spacecraft is controlled by changing the value and direction of the engine thrust. The problem is solved taking into account constraints on the launch time, flight duration, and minimum distance to the Sun.     

A nonvariational approach to multiple finite-burn propellant optimization

In this paper a nonvariational approach to the finite-burn minimum fuel problem is presented. In particular, attention is focused on one of the computer codes of a sophisticated software package at Telespazio for dealing with a fuel minimization under nonlinear equality and inequality constraints. In this program thrust in an inverse-square gravitational field is considered. A short thrusting arc is dealt with by a transition matrix. A long burning arc is segmented in a suitable number of subarcs where the transition matrix formulation holds. Use of appropriate penalty functions allows the mission analyst to consider several equality and inequality constraints. The minimum search algorithm consists of a modified version of the Levenberg-Marquardt method. The overall computer code is able to accept even some rough estimate of the optimal profile. A wide spectrum of transfer flights is presented.     

金属长旋转椭球附近偶极子辐射

本文采用严格的麦克斯韦方程组的直接求解法,分析了金属长旋转椭球附近任意位置电偶极子的辐射特性,并得到辐射场量表达式。最后举例对长旋转椭球侧部的偶极子方向图进行了数值计算并由实验证实其结果。     

Hori method for generalized canonical systems

In this paper, some special features on the canonical version of Hori method, when it is applied to generalized canonical systems (systems of differential equations described by a Hamiltonian function linear in the momenta), are presented. Two different procedures, based on a new approach for the integration theory recently presented for the canonical version, are proposed for determining the new Hamiltonian and the generating function for systems whose differential equations for the coordinates describe a periodic system with one fast phase. These procedures are equivalent and they are directly related to the canonical transformations defined by the general solution of the integrable kernel of the Hamiltonian. They provide the same near-identity transformation for the coordinates obtained through the non-canonical version of Hori method. It is also shown that these procedures are connected to the classic averaging principle through a canonical transformation. As examples, asymptotic solutions of a non-linear oscillations problem and of the elliptic perturbed problem are discussed.     

Thin body motion under free surface with formation of final length cavity

The two-dimensional problem of high velocity moving slender body interaction with fluid free surface was regarded. Gravity was neglected as compared with fluid inertia. The problem is relevant to underwater motion of a bullet or shell, which could take place in orbital collisions of particles with fluid-filled containments. The problem is also relevant to evaluating wave-breakers effect on the streaming flow. The solution was obtained for the case of final length cavity formation behind the body. The solution allows determining free surface shape, drag and lift forces. In the limiting cases of relatively small depth or high compressibility, the obtained solution permitted analytical approximation.     

Symmetric periodic solutions of the Hill’s problem. I

The planar circular Hill’s problem is considered, as well as its limiting integrable variant called the Hénon problem, for which the original Hill’s problem is a singular perturbation. Among solutions to the Hénon problem there are a countable number of generating solutions-arcs that are uniquely determined by the condition of successive passage through the origin of coordinates—singular point of equations of motion of the Hill’s problem. Using the generating solutions-arcs as “letters” of a certain “alphabet”, one can compose, according to some rules, the “words”: generating solutions of families of periodic orbits of the Hill’s problem. The sequence of letters in a word determines the order of orbit transfer from one invariant manifold to another, while the set of all properly specified words determine the system’s symbolic dynamics.     

Optimization of low-thrust transfers in the three body problem

We consider transfers with low thrust in an arbitrary field of forces. The modified method of transporting trajectory [1–4] is used for optimization of the transfers. The complexity of finding the transporting trajectory of a preset type can be the main obstacle to application of this method. This challenge is solved for the three-body problem in the Hill motion model. Numerical analysis of the method is performed using an example of the transfers to halo-orbits around the solar-terrestrial libration points.     

Trajectory Control for a Spacecraft with an Inflatable Braking Device in the Martian Atmosphere

The possibility of using an inflatable braking device for controlled descent in the Martian atmosphere of large-capacity cargoes is analyzed. The most complicated version of the trajectory control problem is considered, namely, the injection of a spacecraft at hyperbolic velocity into a parking orbit after braking in the atmosphere.     

Asymmetric wedging of elastic material with the formation of separation zones

The problem of asymmetrical movement of a thin rigid impactor in elastic material is considered with subsonic and transonic velocities. For all considered range of velocities the flow diagram was determined for contours in the forms of wedge and ogive. There is a limiting speed value when the impactor moves with velocity higher than the speed of transverse wave at which the separation zone in the nasal part of the body disappears. At this velocity forces acting on the impactor are independent of its shape.     

On hydromagnetic flow of an Oldroyd-B fluid near a pulsating plate

An initial value investigation is made of the motion of an incompressible, viscoelastic, conducting Oldroyd-B fluid bounded by an infinite rigid non-conducting plate. The unsteady flow is generated from rest in the fluid due to velocity tooth pulses subjected on the plate in presence of an external magnetic field. It is assumed that no external electric field is acting on the system and the magnetic Reynolds number is very small. The operational method is used to obtain exact solutions for the fluid velocity and the shear stress on the plate. Quantitative analysis of the results are presented with a view to disclose the simultaneous effects of the magnetic field and the fluid elasticity on the flow and the wall shear stress for different periods of pulsation of the plate. It is shown that the classical and hydromagnetic Rayleigh solutions are limiting cases of the present analysis.     

Vertical structure of the magnetic field in active regions of the sun at coronal heights

High-altitude measurements and magnetic field distribution in active regions are always an important problem to verify existing models at heights from units to hundreds of Mm. Optical methods of analysis of the magnetic structure work well only at the photosphere level. At the same time, the progress of radio astronomy methods of analyzing the solar radio emission [1] and of the theory of solar plasma radiation [2] facilitates introduction of new methods for measuring the magnetic field strength at various altitudes in the solar atmosphere. In this paper we use multi-wave observations of polarization of the radio emission of active regions in the microwave range together with precise magnetosphere data in order to develop a method of projection for measuring the height distribution of the magnetic field.     

Analytical solutions that interpret the evolution of dual-frequency space-based systems in the case of orbital Lindblad resonance,taking into account the Rayleigh dissipation: I

As a part of a planetary version of the three-body problem in the orbital dual-frequency first-order resonance, with allowance for the Rayleigh dissipation, analytical solutions are obtained, which interpret the dynamic evolution of the orbital elements of components of the system under consideration.     

The motion of a particle in perturbed field of an attracting center

The integrable case of the perturbed two-body problem is considered. The perturbation is determined by the potential of a special form. The L-matrix is chosen in such a way that partial separation of variables should take place in regular coordinates. Integration of the equations of motion of the problem under consideration is made. The solutions are expressed through elliptic functions. The orbits for various cases are constructed. The results of numerical calculations are given.     

Sunspot oscillations as derived from the <Emphasis Type="Italic">SOHO</Emphasis>/MDI magnetograms

As a result of processing long (up to 144 h) series of sunspot magnetograms obtained on the SOHO (Solar and Heliospheric Observatory) spacecraft with the MDI (Michelson Doppler Imager) instrument it is shown that the mode with a period of 800–1300 min is a limiting low-frequency oscillation mode of the magnetic field of a sunspot as a whole. Its period is essentially and nonlinearly depends on the sunspot magnetic field strength. In addition to this mode, higher harmonics are also revealed in the sunspot oscillation spectra in the bands 40–45, 60–80, 135–170, 220–250, and 480–520 min. The oscillation power in these bands monotonically and rapidly decreases with increasing frequency, which is characteristic for overtones arising due to the nonlinear nature of oscillations. The limiting oscillation mode stably exists in sunspots for 1.5–2 days, which coincides with the average lifetime of a supergranular cell. The mode with the period of 35–48 h observed in the power spectrum is not an eigen mode of sunspots, because its period is independent of its magnetic field strength. Probably, it occurs as a quasiperiod of an external exciting force caused by disturbances from supergranular cells surrounding the sunspot.     

Control of a spacecraft’s spatial turn with minimum value of the path functional

The problem of optimal (with minimum value of the path functional) control over a spatial reorientation of a spacecraft is considered. Using the quaternion method, an analytical solution to this problem is obtained. For the symmetrical optimality index, the complete solution to the problem of spacecraft reorientation is represented in a closed form. The results of mathematical modeling of the spacecraft motion dynamics are presented, demonstrating the practical efficiency of the developed algorithm of control.     

Investigation of Periods of Evolution for Elliptical Orbits in the Double-Averaged Hill Problem

The geometric analysis applied to the solutions obtained by M.L. Lidov [1] of the satellite version of a restricted circular double-averaged three-body problem allowed us fresh view at the comparative analysis of evolution periods for various elliptical orbits. Based on the similarity theory, the parameters of similitude are invoked for orbits and perturbations. An expression for the period of evolution of three orbit elements through the appropriate similitude parameters is derived. On this basis, a regularity is formulated, the consequences of which are analyzed.     

Electrification of a rocket during its launch and motion in the atmosphere along active part of the trajectory

We studied the process of electrification of a rocket during launch and flight in the atmosphere at the active part of its trajectory. The values of charge, field strength, and rocket potential at the launch are estimated. Charging and discharging currents are determined for a rocket flying through clouds and precipitation, and solutions expressing the time variation of the rocket’s charge are found. The values of charge, field strength, and rocket potential are obtained as functions of time, together with the engine plume represented as a charged plasma structure. The rocket’s charge is shown to tend to an equilibrium state, and the time of reaching it is found. Mechanisms limiting the charge value are considered, and the conditions of origination of an electric breakdown (lightning) between the rocket and atmosphere are determined.