Simple method for performance evaluation of multistage rockets

Multistage rockets are commonly employed to place spacecraft and satellites in their operational orbits. Performance evaluation of multistage rockets is aimed at defining the maximum payload mass at orbit injection, for specified structural, propulsive, and aerodynamic data of the launch vehicle. This work proposes a simple method for a fast performance evaluation of multistage rockets. The technique at hand is based on three steps: (i) the flight-path angle at each stage separation is guessed, (ii) the spacecraft velocity is maximized at the first and second stage separation, and (iii) for the last stage the thrust direction is obtained through the particle swarm optimization technique, in conjunction with the use of the Euler–Lagrange equations and the Pontryagin minimum principle. The coast duration at the second stage separation is optimized as well. The method at hand is extremely simple and easy-to-implement, but nevertheless it proves to be capable of yielding near-optimal ascending trajectories for a multistage launch vehicle with realistic structural, propulsive, and aerodynamic characteristics. The solutions found with the technique under consideration can be employed either for a rapid evaluation of the multistage rocket performance or as guesses for more refined optimization algorithms.     

基于模糊神经网络的质量矩拦截弹动态逆控制

质量矩控制是一种全新的飞行控制方法,与广泛应用的空气动力控制相比,可以避免飞行器在超高马赫数飞行时舵面的气动加热问题,而且,可以提高飞行器的机动性和敏捷性。以所建立的质量矩拦截弹数学模型为基础,通过对模型合理的简化,得到一个耦合的非线性动力学系统。考虑到系统的鲁棒性要求和三个滑块的协调控制问题,应用双时标分解的方法,提出将拦截弹动力学分离为快变状态动力学和慢变状态动力学。然后,设计了拦截弹模糊动态逆飞行控制系统,分别针对快变和慢变子系统,提出了一种基于模糊神经网络(FNN)的动态逆误差补偿方法,可以有效地抑制气动参数摄动而引起的控制系统性能的下降,提高了控制系统的鲁棒性。仿真结果表明系统性能指标满足设计要求,只需微调滑块位置,即可以实现拦截弹的飞行控制。     

BTT导弹控制系统鲁棒动态逆设计

应用双时标的假设计，将导简动力学分离为快变状态动力学和慢变状态动力学，然后，对慢变动力学和快变动力学分别进行反馈线性化设计，考虑到空气动力系数具有较大的不确定性，进一步，对期望的慢变动力学和快变动力学进行鲁棒控制设计，6DOF数学仿真验证了该方法的有效性。     

A study of evolution of spin-up mode of a satellite in the plane of its orbit

We investigate the mode of spinning up a low-orbit satellite in the plane of its orbit. In this mode the satellite rotates around its principal central axis of the minimum moment of inertia which executes small oscillations with respect to the normal to the orbit plane; the angular velocity of the rotation around this axis several times exceeds the mean orbital motion. Gravitational and restoring aerodynamic moments are taken into account in the satellite’s equations of motion. A small parameter characterizing deviation of the satellite from a dynamically symmetric shape is introduced into the equations. A two-dimensional integral surface of the equations of motion, describing quasi-steady-state rotations of the satellite close to cylindrical precession of the corresponding symmetrical satellite in a gravitational field, has been studied by the method of small parameter and numerically. Such quasi-steady-state rotations are suggested to be considered as unperturbed motions of the satellite in the spin-up mode. Investigation of the integral surface is reduced to numerical solution of a periodic boundary value problem of a certain auxiliary system of differential equations and to calculation of quasi-steady-state rotations by the two-cycle method. A possibility is demonstrated to construct quasi-steady rotations by way of minimization of a special quadratic functional.     

空空导弹大角度姿态推力矢量控制研究

为研究具有大离轴角及越肩发射能力的先进空空导弹敏捷转弯方法，研究了空空导弹的大角度姿态机动控制律。利用时间尺度分离的方法将导弹的姿态动力学和运动学系统分别看做快子系统和慢子系统。用李亚普诺夫方法设计了慢子系统控制律。利用动态逆方法设计了快子系统控制律。分析了控制系统的鲁棒性和稳态精度。仿真结果证明了所提控制方法能够大大减小空空导弹大角度姿态机动时各种力矩干扰的影响。最后给出了采用姿态控制实现的越肩发射的仿真结果。     

Evolution of Rotational Motion of a Symmetrical Satellite with Viscoelastic Rods

We study the motion of a symmetrical satellite with a pair of flexible viscoelastic rods in a central Newtonian gravitational field. A restricted problem formulation is considered, when the satellite's center of mass moves along a fixed circular orbit. A small parameter is introduced which is inversely proportional to the stiffness of flexible elements. Another small parameter is equal to the ratio of the squared orbital angular velocity and the squared magnitude of the initial angular velocity of the satellite. In order to describe the satellite rotational motion relative to the center of mass, we use the canonical Andoyer variables. In the undisturbed formulation of the problem, i.e., at = 0 and = 0, these variables are the action–angle variables. Equations describing the evolution of motion are derived by an asymptotic method which combines the method of separating motions for systems with an infinite number of degrees of freedom and the Krylov–Bogolyubov method for systems with fast and slow variables. The manifolds of stationary motions are found, and their stability is investigated on the basis of equations in variations. Phase portraits are constructed which describe the rotational motion of a satellite at the stage of slow dissipative evolution.     

返回器稀薄区气动特性工程计算方法的应用研究

中国航天返回器再入过程采用非弹道式再入轨道,其高空稀薄区滞留时间显著增长,稀薄效应对再入飞行的影响显著增强,因此快速而准确地预测返回器稀薄区气动特性变得非常重要。文章分析归纳了多种稀薄区气动特性工程计算方法即桥函数方法的发展和应用,并以 Stardust 返回舱为对象,对比分析了三种不同桥函数的预测精度,给出了在航天返回器气动预测中更为合适的工程方法。结果显示：不同桥函数预测结果差别很大;在不同攻角下,与数值模拟的对比分析表明,局部桥函数方法气动特性预测结果基本优于其它桥函数,尤其是在力矩系数预测上。因此稀薄区气动特性的预测采用局部桥函数较为合适。     

Post-aerocapture orbit selection and maintenance for the Aerofast mission to Mars

Aerofast is the abbreviation of “aerocapture for future space transportation” and represents a project aimed at developing aerocapture techniques with regard to an interplanetary mission to Mars, in the context of the 7th Framework Program, with the financial support of the European Union. This paper describes the fundamental characteristics of the operational orbit after aerocapture for the mission of interest, as well as the related maintenance strategy. The final orbit selection depends on the desired lighting conditions, maximum revisit time of specific target regions, and feasibility of the orbit maintenance strategy. A sunsynchronous, frozen, repeating-ground-track orbit is chosen. First, the period of repetition is such that adjacent ascending node crossings (over the Mars surface) have a separation compatible with the swath of the optical payload. Secondly, the sunsynchronism condition ensures that a given latitude is periodically visited at the same local time, which condition is essential for comparing images of the same region at different epochs. Lastly, the fulfillment of the frozen condition guarantees improved orbit stability with respect to perturbations due to the zonal harmonics of Mars gravitational field. These three fundamental features of the operational orbit lead to determining its mean orbital elements. The evaluation of short and long period effects (e.g., those due to the sectorial harmonics of the gravitational field or to the aerodynamic drag) requires the determination of the osculating orbital elements at an initial reference time. This research describes a simple and accurate approach that leads to numerically determining these initial values, without employing complicated analytical developments. Numerical simulations demonstrate the long-period stability of the orbit when a significant number of harmonics of the gravitational field are taken into account. However, aerodynamic drag produces a relatively slow orbital decay at the altitudes considered for the mission. This circumstance implies the progressive loss of the sunsynchronism condition, and therefore corrective maneuvers are to be performed. This work proves that actually only in-plane maneuvers are necessary, evaluates the overall delta-v budget needed in the period of repetition (85 Martian nodal days), and proposes a simple maintenance strategy, making reference to the worst-case scenario, which corresponds to the highest seasonal values of the atmospheric density and to the maximum value of the ballistic coefficient of the spacecraft.     

大尺度薄壁结构力-热-电一体化分析

基于有限元-多层快速多级子方法(FEM-MLFMM)提出天线罩力热电一体化分析方法,以平板为研究对象,验证一体化分析方法的准确性;以大尺度升力天线罩为研究对象,开展气动力和气动热载荷下结构的力-热-电一体化分析,评估力/热环境下结构的强度性能,并探究力/热载荷对结构电磁透波性能的影响规律.研究结果表明:提出的一体化分析...     

气动载荷对整流罩分离特性影响的仿真计算研究

文章利用有限元软件Abaqus中的流-固耦合分析模块CEL仿真计算了整流罩平抛分离过程,对比研究了气动载荷对整流罩分离过程的影响,并与试验进行了对比。结果表明,计算与试验结果吻合较好,分离初始时刻罩内负压所产生的气动载荷严重阻碍整流罩的正常分离,造成整流罩与内部有效载荷的碰撞干涉。仿真计算可为今后整流罩地面分离试验验证提供新的途径。     

考虑复合控制系统动态特性的前向拦截制导律

为满足临近空间拦截高速大机动目标的实际需求,研究了考虑直接力/气动力复合控制动态特性的前向拦截制导律设计方法。在考虑连续气动力和离散直接力特点的基础上,给出了一种在气动舵控制基础上设计连续直接力、然后通过冲量等效法进行离散化的直接力设计方法,避免了复杂的控制分配问题。根据二维前向拦截导引运动学模型和拦截导弹动力学模型,利用时间尺度分离,将拦截导弹和目标的质点运动学与加速度慢变子系统构成的动态系统,看成慢变子系统,设计了俯仰角速度指令;将俯仰角速度动态子系统看成快变子系统,通过对俯仰角速度指令的跟踪控制设计得到考虑复合控制系统动态特性的前向拦截导引律。仿真结果校验了本文方法的正确性和有效性。     

Transition of Planar Rotational Motion of an Asymmetric Spacecraft into Oscillatory Motion at Its Reentry into the Atmosphere

The motion of a spacecraft with small asymmetry relative to its center of mass is considered. The restoring aerodynamic moment of the spacecraft is described by the Fourier series in terms of the angle of attack with the two first sinusoidal and the first cosinusoidal terms. A solution for the angle of attack in the undisturbed rotational motion is found. The analytical expression is obtained for the integral of action taken along the separatrices that separate the rotational and oscillatory regions of the phase portrait of a system. The transition of the spacecraft's motion from planar rotational to oscillatory is investigated. This transition is caused by a slow variation of moment characteristic coefficients, as well as by the presence of small asymmetry and damping and slow variation of their coefficients. Analytical formulas are obtained for determining the times of transition from rotational to oscillatory motion, as well as for the critical angular velocity of beyond-the-atmosphere rotation. When this critical velocity is exceeded, body rotation proceeds for a long time interval (planar autorotation arises).     

考虑高空粘性干扰效应的乘波体气动性能工程预测方法研究

粘性干扰效应是飞行器在高空、高马赫数飞行状态下所面临的诸多重要物理效应之一,对飞行器在这一区段飞行时的气动性能有着极其重要的影响.本文基于粘性干扰理论,结合参考温度方法提出了一种能够考虑粘性干扰效应的高超声速乘波体气动性能的工程预测方法,克服了传统工程预测方法不能计及粘性干扰效应的不足.文中对该方法的合理性进行了理论分析,并在飞行高度30～70km,飞行马赫数15～20范围内,通过本文提出的方法与传统工程方法以及计算流体力学(CFD)方法计算结果的比较,验证了本文所提出的方法的有效性.     

Motion of deformable planets and stability of their stationary rotations

A mechanical system consisting from N deformable spheres interacting according to the law of gravity is considered as a model of planetary system. Deformations of the viscoelastic spheres are described according to the model of the theory of elasticity of small deformations, the Kelvin-Voigt model of viscous forces, and occur under the action of gravitational fields and fields of centrifugal forces. Approximate equations describing motions of the centers of mass of the spheres and their rotations relative to the centers of mass are constructed by the method of separation of motions on the basis of solving quasistatic problems of the theory of viscoelasticity with allowance made for smallness of sphere deformations. Using the first integral of conservation of the angular momentum of the system relative to its center of mass, the expression for the changed potential energy is obtained with the use of the Routh method. An investigation of stationary rotations is carried out, and it is shown that all of them are unstable, if the number of planets is more than two.     

One method of gravitational attitude control of a rotating satellite

The mode of spinning up a low-orbit satellite in the plane of its orbit is studied. In this mode, the satellite rotates around its longitudinal axis (principal central axis of the minimum moment of inertia), which executes small oscillations with respect to the normal to the orbit plane; the angular velocity of the rotation around the longitudinal axis is several tenths of a degree per second. Gravitational and restoring aerodynamic moments were taken into account in the equations of satellite’s motion, as well as a dissipative moment from eddy currents induced in the shell of the satellite by the Earth’s magnetic field. A small parameter characterizing deviation of the satellite from a dynamically symmetric shape and nongravitational external moments are introduced into the equations. A two-dimensional integral surface of the equations of motion, describing quasistationary rotations of the satellite close to cylindrical precession of the corresponding symmetrical satellite in a gravitational field, has been studied by the method of small parameter and numerically. We propose to consider such quasistationary rotations as unperturbed motions of the satellite in the spin-up mode.     

卫星主动段动力学环境数据分析

某型号小卫星发射时,用搭载的测量系统对星上6个测点位置进行了3个方向的振动响应测量,获得了主动段2000 Hz范围内的完整数据。数据分析表明,小卫星主动段的振动模态特性和振动响应特性不同于地面模拟试验中的结果,主要体现在:主动段40 Hz处的Pogo效应明显;共振频率与地面试验完全不同;横向响应量级明显小于纵向响应量级;在小于2000 Hz频率范围内,星箭分离冲击对星上测点位置影响很小。与地面试验数据的对比分析结果表明,目前的地面振动试验方法仍有不足,存在过试验或欠试验。     

The solution of a model problem of the atmospheric entry of a small meteoroid

Direct simulation Monte Carlo modeling (DSMC) is used to solve the problem of the entry into the Earth’s atmosphere of a small meteoroid. The main aspects of the physical theory of meteors, such as mass loss (ablation) and effects of aerodynamic and thermal shielding, are considered based on the numerical solution of the model problem of the atmospheric entry of an iron meteoroid. The DSMC makes it possible to obtain insight into the structure of the disturbed area around the meteoroid (coma) and trace its evolution depending on entry velocity and height (Knudsen number) in a transitional flow regime where calculation methods used for free molecular and continuum regimes are inapplicable.     

某高亚声速鸭式导弹超临界对称翼型设计研究

为改善高亚声速导弹气动性能,提出了超临界对称翼型概念。该翼型具有前缘钝圆,表面平坦,型面面积大等特点。在跨声速、小攻角状态下,翼型表面大部分区域为超声速区,有效防止了激波出现并减轻了边界层分离程度,进而提高了阻力发散马赫数和升阻比。针对某高亚声速鸭式导弹,采用CFD(computational fluid dynamic)软件求解N-S(Navier-Stokes)方程的方法和基于翼型特征的参数描述(PARSEC)方法优化设计了一种超临界对称翼型,并将其应用于鸭舵和尾翼设计。最后,进行了导弹全弹外形的跨声速风洞试验。结果表明:使用超临界对称翼型的高亚声速导弹具有良好的升阻特性。     

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。     

天问一号着陆器大底分离触发条件设计方法

针对天问一号着陆器防热大底分离触发条件确定问题,利用数学仿真的方法分析气动特性、防热大底相对着陆器姿态运动等因素对分离安全性的影响,给出可安全分离的触发条件.不同分离触发马赫数的仿真结果表明,较大分离马赫数的碰撞风险较高,但防热大底长期运动趋势由弹道系数决定,相比着陆器下降更快.根据伞降过程着陆器姿态运动及伞绳力特点,...