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].     

Theory of type III radio bursts in the interplanetary space. II. Study of instability of the electron beam-solar wind plasma system in a linear approximation

Frequency characteristics of disturbances of a one-dimensionally inhomogeneous electron beam-solar wind plasma system are studied in the geometrical optics approximation on the basis of the Maxwell equations closed by the material equation obtained earlier. The corresponding dispersion equation is derived and solved. It is found that resonance interaction of a wave with an electron beam can occur only at two spatial points. Perhaps, such a short-time (point-like) mechanism of the resonance clarifies one of the main problems of physics of electron beams generated by solar flares: their time of existence is much longer than the time following from the previous theoretical estimates of the beam energy loss rate due to radiation.     

航天器共振轨道研究

建立航天器非开普勒运动理论是航天技术发展的必然。提出了一类非开普勒轨道——共振轨 道。共振是自然界的一种普遍现象,当发生共振时,很小的输入可以使系统的状态产生较大 变化。研究表明航天器在推力作用下的非开普勒运动在参数平面内可以视为一种受迫振 动,也会发生共振现象。因此,可以利用共振原理来研究航天器的运动,称这样一类非开普 勒轨道为共振轨道。首先通过合理地选择轨道描述参数、时间尺度和推力描述方式建立 航天器共振轨道的动力学模型。然后讨论航天器在推力作用下轨道运动的振动规律,并给出 共振轨道的概念及轨道方程。最后提出基于共振轨道的机动轨道设计方法。
     

展开式卫星天线在发射时的非线性振动分析

本文利用有限元数值计算与解析分析相结合的方法，研究了展开式卫星天线在收拢状态（发射阶段）的非线性动力学特性，论述了平面外扭弯耦合东振（存在间隙时）及平面内渗、强亚谐共振时的非线性特性。得到了间隙对扭弯共振的影响变化曲线及产生参、强亚谐共振的条件，本文结论可作为工程设计的理论依据。     

Optimal transfer from the lagrangian points

The transfer from the equilateral Lagrangian points of the Earth-Moon system is analysed. The final states of the velocity of the space vehicles and of the rotation velocity of the propulsion vector are assumed given. The trajectory which ensures the transfer in optimal time consists of three arcs. On this trajectory the rotation velocity of the direction of the propulsion has the extremal value or corresponds to the Lawden's tangent law. The use of the matching of the arcs together with transversality conditions and final conditions determines the constants of integration and the evolution time. The resulting parametric equations of the optimal trajectory are of integral form.     

动态无线能量传输系统参数化设计与优化

无线能量传输技术以其操作方便快捷、适应快速更换及维修、减少机动作业无缆影响、可快速扩展、大幅减小设备电池质量、无触电危险、极限环境适应性强等特点被广泛应用于各领域。针对给定输入和约束,要求对动态无线能量传输系统的耦合机构尺寸和电路参数进行充分优化设计以满足一定输出功率效率的需求。经过前期对电路和耦合机构磁路的理论及仿真研究,得到了系统各参数变化时将导致系统输出特性随之如何变化的理论依据。基于此,建立了动态无线能量传输系统的参数化设计模型,并进行优化设计流程及步骤,以最简化的计算流程和最少的工作量,实现了动态无线能量传输系统的发射轨道和电路的参数化设计。该研究将对动态无线能量传输系统的多目标多参数化自动最优化设计具有重要的指导意义。     

吸气式高超声速飞行器机体推进控制一体化建模方法研究

针对吸气式高超声速飞行器气动力、气动热、结构、推进、飞行轨迹以及姿态之间的多物理场强耦合给飞行控制系统设计带来的问题,提出一种适用于此类飞行器机体/推进/控制一体化设计的建模方法.首先,依据类乘波体高超声速飞行器基本外形参数体系设计飞行器的三维外形;然后在飞行器流场分析的基础上,给出飞行控制系统需要满足的姿态约束条件,并采用一套完整的工程预测方法建立了适合进行飞行控制一体化设计的气动力/推力耦合模型;最后基于拉格朗日方程推导了一体化弹性体动力学模型.模型算例验证了该方法在吸气式高超声速飞行器机体/推进/控制一体化设计中的可行性.     

Parametric resonance in the solar corona

When studying microwave emission of active regions on the Sun, an effect of parametric resonance between 5-min velocity oscillations in the solar photosphere and sound oscillations of coronal magnetic loops modulating the microwave emission has been discovered for the first time. The effect shows itself as simultaneous excitation in coronal magnetic loop of oscillations with periods 5, 10, and 3 min, which correspond to the pumping frequency, subharmonic, and the first upper frequency of parametric resonance. The parametric resonance can serve as an effective channel of transporting the energy of photospheric oscillations into the upper layers of the solar atmosphere. This effect opens up the important prospects in understanding the mechanisms of coronal plasma heating.     

基于参数化外形的通用大气飞行器建模与分析

提出了一类翼身组合升力体外形通用大气飞行器(Common Aero Vehicle, CAV)的参数化外形建模方法,采用气动工程预估方法计算CAV的气动系数,拟合得到能用于再入飞行器制导与控制仿真的气动模型,并通过分析,得到该模型静稳定性、气动效率及气动控制特性等方面的结论。结合飞行器再入飞行的运动方程,选取平衡工作点,基于小扰动线性化模型得到系统特征根分布来分析其稳定性,发现固定姿态的滑翔飞行时系统有正半平面极点,需主动控制调节;为了分析机动性,提出了以星下点轨迹曲率求取CAV转弯半径的方法,可快速获取机动性评估与参考指标,结果表明,该模型具有较好的转弯机动能力。     

Variational equations in parametric variables and transformation of their solutions

An analytical relationship is derived which connects the matrix of partial derivatives of the current state vector with respect to the initial conditions with the matrix of solutions to variational equations in parametric variables. These equations correspond to the equations of motion obtained using the generalized coordinate-time transformation admitting an increase of the number of unknown parameters. Particular cases of transformations leading to the variational equations in regularizing variables of Sperling-Burdet and Kustaancheimo-Stiefel are considered. All formulas necessary in these cases for determination of the matrix of isochronous derivatives are obtained.     

基于DSM的航天器信息建模方法及应用

将设计结构矩阵（DSM）技术应用于航天器研制的设计流程建模和信息建模,能够清晰准确地描述航天器各设计活动之间的信息耦合关系。根据航天器设计过程中跨分系统集成和协同设计的具体教学与培训需求,开发了一种基于DSM进行建模的工具软件,可用于建立一个基于设计参数信息的集成设计系统。根据其内在耦合关联关系,可实现各个分系统、各个模块、各个学科的参数信息一致和动态关联更新。     

Evolution of asteroid orbits at the 3 : 1 their mean motion resonance with Jupiter (planar problem)

The 3 : 1 mean motion resonance is studied in the planar elliptic restricted three-body problem (Sun-Jupiter-asteroid). Using double numerical averaging, the equations are constructed that describe the secular evolution of eccentricity and perihelion longitude of the asteroid orbit. The region of adiabatic chaos is isolated in the phase space of the system under study.     

旋转充液系统全飞行过程非线性动力学仿真

本文考虑一类刚认耦合的旋转充液系统的飞行动力学问题，在依据力学变分原理给出基本方程，导出全飞行过程运动状态方程的基础上，建立了相应的仿真模型。可能通过对Navier-Stokes方程求解和液体流动的惯性波振动特性，给出液体的反作用力矩。经过仿真实验，分析角运动的时间序列，给出了比较详尽的飞行不稳定机制分析结果。     

Estimation of the Probability of Capture into a Resonance Mode of Motion for a Spacecraft during Its Descent in the Atmosphere

The estimation of the probability of capture into a resonance mode of motion is considered for a spacecraft with a small asymmetry during its entry into the atmosphere. It is assumed that the initial conditions of spacecraft motion are distributed uniformly in some sufficiently small domain. The problem is solved for the equations of spacecraft motion linear with respect to the angle of attack. An analytical estimate of the probability of the spacecraft capture into the resonance corresponding to an ascending branch of the velocity head is obtained. The emphasis in the analysis of the estimate is made on the effect of the spacecraft asymmetry type on the probability of capture. A comparison of the estimate with the results of numerical computation is carried out. A model problem concerning the construction of the domain of the spacecraft center of mass locations, most dangerous from the point of view of the realization of the stable resonant modes of motion, is solved.     

再入弹头非对称气动力研究

本文通过六自由度弹道方程数值模拟了再入弹头非对称气动力和非对称静、动导数对弹头滚转异常的影响;阐述了非对称气动力及非对称静、动导数产生的机理。本文利用作者建立的近似计算和数值计算方法,计算了典型的非对称再入弹头的气动力,定性分析了非对称气动力随弹头几何参数的变化规律,对再入弹头设计有重要的参考价值。     

The derivation of a second-order satellite trajectory predictor in terms of geometrical variables

This paper develops a new semianalytic theory by generalization of the Method of Averaging (MoA) and the Stroboscopic Method (SM). Unlike the traditional development of the MoA, which must use the mean anomaly, this new approach can treat any orbital anomaly. In particular, a more geometrically significant position variable, the true anomaly, is considered here. This extension of the traditional methods presents significant analytical and numerical advantages. For instance, the averaging of the rate functions does not require the usual change of variable to true anomaly and the evaluation of the short-period terms does not involve the solution of the transcendental Kepler equation. The new set of differential equations is completely independent of the satellite anomalistic motion, thus allowing the propagation of the state with a relatively large (up to a few days) integration stepsize. This feature effectively increases the flexibility of the SM, which normally restricts the propagation of the state to integral multiples fo the orbital period. The transformations that relate this new set of averaged rate functions and short-period terms to the traditional ones are derived in a series of analytic expressions called Equivalence Relations. These relations allow a successful comparison of this theory with the classical results found in the literature. Further changes of independent variables to “mean time” and “mean orbit number” naturally lead to difference equations and multirevolution integration algorithms.The principles of this theory are applied to the equations that describe the motion of an earth satellite subjected to gravity (J₂, J₃ and J₄ harmonics) and drag perturbations. The atmospheric model includes the effects of solar and geomagnetic activity, the diurnal, semiannual and seasonal-latitudinal cycles of density variations and the flattening and rotation of the atmosphere. The short-period oscillatory terms and the averaged differential equations associated with these perturbations are developed into completely analytical expressions. This feature provides insights into the dynamics of the satellite and simplifies the numerics of the prediction process. Numerical simulation of this new set of differential equations and comparison with the propagation of the unaveraged (osculating) set of differential equations show that the predictor proposed in this paper significantly increases computation speed without loss in accuracy.This theory has been used to predict the orbital lifetime of actual satellites and to conduct a parametric analysis of satellite orbital lifetime.     

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.     

控制输入受限情况下卫星姿态的鲁棒自适应控制

卫星通常工作在各种扰动环境中，包括参数不确定性和非参数不确定性。工程实践中碰到的另一个重要问题是控制输入受限。考虑存在参数不确定性和非参数不确定性，研究控制输入受限情况下卫星的姿态控制问题，设计了一种鲁棒自适应控制器，证明了姿态控制系统是全局一致最终有界稳定。仿真结果验证了该控制器的有效性。     

Comparison of the rocket engines efficiency in the case of low thrust orbit-to-orbit transfers

The main task of this paper is to compare two types of low thrust rocket engines: constant thrust vs. variable-thrust engines. We will be concerned with efficiency, where efficiency is evaluated in the case of the orbit-to-orbit transfer with maximum payload mass in the central Newtonian gravity field. The launch mass of the space vehicle is supposed to be fixed. The traditional solution is the decomposition of the problem into parametric and dynamical parts. The corresponding variational problems differ for two rocket thruster types under consideration. We propose change of variables, which makes it possible to reduce averaged equations of optimal motion of a spacecraft with the mentioned engines to the unified form. Using this unified form comparison of the performance of constant- and variable-thrust engines is conducted.