反舰导弹典型运动建模与仿真

针对现代反舰导弹突防技术的不断发展和舰艇对空防御形势的日益严峻,为提高反舰导弹的探测和识别的准确性,在分析反舰导弹典型运动特性的基础上,采用动力学建模的方法研究弹道问题,把导弹视为可控质点,将过载引入描述导弹质心运动的动力学方程,建立了简洁实用的反舰导弹典型运动模型,并对比例导引运动、蛇行机动、跃升俯冲运动等做了仿真。仿真结果可直观显示反舰导弹的典型运动的弹道特性,验证了所建立的弹道模型对探测、识别和跟踪反舰导弹技术的研究有一定的参考价值。     

非标准气象条件下空地导弹高抛弹道仿真研究

为研究非标准气象因素对导弹运动特性的影响,将大气运动基本方程组同经典弹道模型相结合,建立非标准气象条件下的高抛弹道模型。同时给出大气运动基本方程组易于编程计算的数值解法,采用变步长的四阶龙格库塔数值积分算法,联立大气运动基本方程组求解空地导弹的动力学方程和运动学方程,得到非标准气象条件下导弹弹道的落点坐标(205 65.8,0,-1 389),结果证明了在不同气象条件下导弹的飞行轨迹不同。使用仿真软件STK、卫星工具包可视化三维建模模块实现了某空地导弹从发射至目标攻击阶段的视景仿真,获得了逼真的效果。     

弹道导弹极限能量弹道的求解与仿真

弹道导弹的弹道运动可以看作是导弹绕地心质点的二体运动,在经过发射点到落点的多个椭圆弹道中,发射速度最小的弹道称为最小能量弹道。一般来讲,随着发射速度的增大弹道落点速度和俯角都会增大,因此较高的发射速度可以提高导弹的末端突防概率。在椭圆轨道扁心率与轨道参数关系的研究基础上,研究提出了极限能量弹道轨道根数的求解方法,并进行了仿真开发和实现。理论和仿真结果证明了依靠提高发射速度来增大落点速度和俯角推断的正确性。     

战术弹道导弹的弹道仿真

战术弹道导弹（TBM）的弹道运动可以看作是导弹绕地心质点的二体运动,因此进行TBM弹道仿真的关键是根据发射点和落点的经纬度计算弹道轨道根数。考虑导弹运动过程中地球自转所产生的落点经度的变化,研究建立了弹道轨道根数的求解方法,通过坐标变化方法对轨道根数进行了校验,并采用二体椭圆轨道运动理论实现了TBM的弹道仿真,仿真得到的发射点落点位置与给定的位置完全重合,从而对轨道根数进行了进一步的确认。     

基于滑模趋近律的防空导弹垂直发射姿态控制研究

为了实现一种针对光纤制导的低空战术防空导弹垂直发射过程的姿态控制,首先利用四元数在弹体坐标系下对垂直发射的防空导弹建立了运动方程,并在纵向通道利用小扰动线性化理论将运动方程简化为状态空间模型,然后设计了基于滑模趋近律的姿态控制律,最后建立了Simulink六自由度弹道仿真模型并进行了数字仿真验证,结果表明:基于四元数的运动方程形式运行有效,基于滑模趋近律的姿态控制律可实现对防空导弹垂直发射的有效控制.     

MATLAB在弹道仿真中的应用

在导弹的设计、研究中,弹道仿真是一项必不可少的实验工具.如何能够高效地运用Matlab软件进行弹道全数字仿真是文中主要探讨的问题.针对这一问题,首先分析了弹道仿真数学模型的特点,并以滑翔增程弹为例,详细研究了在M文件、simulink工具箱以及两者交互使用环境下建立外弹道质心运动系统仿真模型的方法和优缺点.最后给出了一定条件下的弹道仿真结果,以此证明该仿真算法对弹道进行仿真研究具有模型设计简单、参数易于修改和结果直观等特点.     

基于复合制导的中/远距空空导弹仿真

中/远距空空导弹攻击距离远、杀伤力强,成为空战致命武器,弹道轨迹和攻击区的解算是对其仿真研究的核心内容.由于空空导弹大都采用复合制导,初始阶段采用惯性导航法,末段采用雷达制导或红外制导,仿真研究复杂且精度较差.为此提出将惯性导航部分分为机载计算机输出轨迹模型和无线电修正,忽略了惯导内部复杂的制导机理.采用比例导引法和运动方程相结合,同时充分考虑导弹速度特性和可用过载,使仿真简单易行.进行了惯导加红外制导导弹仿真,结果表明,就弹道轨迹和攻击区与真实导弹进行比较,改进算法简化了运算过程,提高了精度,具有有效性.     

潜空战术导弹纵向特性分析及控制系统设计

对潜空战术导弹的水下和空中运动分别建立了纵向质心运动方程,分析了出水前后的弹体纵向特性并完成了经典方法的控制系统设计,最后分别给出了Simulink质心弹道和六自由度弹道对比仿真验证;结果表明,潜空导弹质心运动方程可简捷有效地设计期望弹道和分析弹体特性,据此设计出的控制系统可以顺利实现对潜空导弹的全程控制,提供了一套完整的潜空战术导弹纵向特性分析方法和控制系统设计方法。     

直接力/气动力复合控制导弹鲁棒驾驶仪设计

针对防空导弹性能问题,为了有效抑制侧向喷流干扰效应的影响,提高操纵效率和快速响应性,提出了基于L2增益理论进行了直接力/气动力复合控制导弹的导弹自动驾驶仪设计方法.根据L2增益的标准设计线性系统的L2增益设计思想,给出基于代数Riccati方程的求解方法.按直接力/气动力复合控制导弹的法向过载自动驾驶仪结构给出系统的状态空间,将侧向喷流干扰效应作有界干扰,利用全维状态反馈将自动驾驶仪设计问题转换成一个L2增益的标准设计问题,并进行了仿真.结果表明设计的自动驾驶仪指令跟踪精度高,鲁棒性强,实现了干扰的抑制.     

步兵战车反坦克导弹三点法导引弹道视景仿真

针对现有步兵战车反坦克导弹模拟训练器存在的弹道仿真不真实,战场环境不逼真的问题.依据三点法导引规律建立导弹的弹道模型,在MATLAB软件下实现弹道的数值仿真计算.构建步兵战车、三维地形和反坦克导弹的实体模型,以虚拟现实软件Vega作为核心图形引擎实现反坦克导弹攻击过程的视景仿真,使训练人员能够直观地观察导弹飞行状态及命中目标后的毁伤效果.采用多分辨率LOD地形分割算法对战场环境进行优化,在一定程度上解决了大规模地形在逼真度和仿真实时性上难以兼顾的问题.研究可为增强训练系统的逼真度提供一个切实可行的方法,对提高模拟器的训练效果具有重要的现实意义.     

Delay dependent estimates for waveform relaxation methods for neutral differential-functional systems

In this paper, the problem of delay dependent error estimates for waveform relaxation methods applied to Volterra type systems of functional-differential equations of neutral type including systems of differential-algebraic equations is discussed. Under a Lipschitz condition (with delay dependent right-hand side) imposed on the so-called splitting function it is shown how the error estimates depend on the character of delays and that for this reason they are better than the known error estimates for relaxation methods. It is proved that under some assumptions the exact solution can be obtained after a finite number of steps of the iterative process, i.e., we prove that the waveform relaxation methods have the same property as the classical method of steps for solving delay-differential equations with nonvanishing delays. We also show the convergence of the waveform relaxation method without assuming that the spectral radius of the corresponding matrix related to the Lipschitz coefficients for the neutral argument is less than one.     

Constraint-Defined Manifolds: a Legacy Code Approach to Low-Dimensional Computation

If the dynamics of an evolutionary differential equation system possess a low-dimensional, attracting, slow manifold, there are many advantages to using this manifold to perform computations for long term dynamics, locating features such as stationary points, limit cycles, or bifurcations. Approximating the slow manifold, however, may be computationally as challenging as the original problem. If the system is defined by a legacy simulation code or a microscopic simulator, it may be impossible to perform the manipulations needed to directly approximate the slow manifold. In this paper we demonstrate that with the knowledge only of a set of “slow” variables that can be used to parameterize the slow manifold, we can conveniently compute, using a legacy simulator, on a nearby manifold. Forward and reverse integration, as well as the location of fixed points are illustrated for a discretization of the Chafee-Infante PDE for parameter values for which an Inertial Manifold is known to exist, and can be used to validate the computational results     

Constraint-defined manifolds: A legacy code approach to low-dimensional computation

If the dynamics of an evolutionary differential equation system possess a low-dimensional, attracting, slow manifold, there are many advantages to using this manifold to perform computations for long term dynamics, locating features such as stationary points, limit cycles, or bifurcations. Approximating the slow manifold, however, may be computationally as challenging as the original problem. If the system is defined by a legacy simulation code or a microscopic simulator, it may be impossible to perform the manipulations needed to directly approximate the slow manifold. In this paper we demonstrate that with the knowledge only of a set of “slow” variables that can be used toparameterize the slow manifold, we can conveniently compute, using a legacy simulator, on a nearby manifold. Forward and reverse integration, as well as the location of fixed points are illustrated for a discretization of the Chafee-Infante PDE for parameter values for which an Inertial Manifold is known to exist, and can be used to validate the computational results.     

Stability of Neutral Impulsive Nonlinear Stochastic Evolution Equations with Time Varying Delays

In this paper, we consider the stability of mild solutions to neutral impulsive nonlinear stochastic evolution equations with time varying delays. With the non‐Lipschitz condition, the Lipschitz condition being taken as a special case, on the impulsive term, the existence, uniqueness and sufficient conditions for the exponential stability in the pth moment and the almost sure exponential stability of the mild solutions are derived by employing a fixed point approach. An example is provided to illustrate the efficiency of the obtained theorems.     

Approximate solution of a class of linear integro-differential equations by Taylor expansion method

In this paper, a simple and effective Taylor expansion method is presented for solving a class of linear integro-differential equations including those of Fredholm and of Volterra types. By means of the nth-order Taylor expansion of an unknown function at an arbitrary point, a linear integro-differential equation can be converted approximately to a system of linear equations for the unknown function itself and its first n derivatives under initial conditions. The nth-order approximate solution is exact for a polynomial of degree equal to or less than n. Some examples are given to illustrate the accuracy of this method.     

Instability in supercritical nonlinear wave equations: Theoretical results and symplectic integration

Nonlinear wave evolutions involve a dynamical balance between linear dispersive spreading of the waves and nonlinear self-interaction of the waves. In sub-critical settings, the dispersive spreading is stronger and therefore solutions are expected to exist globally in time. We show that in the supercritical case, the nonlinear self-interaction of the waves is much stronger. This leads to some sort of instability of the waves. The proofs are based on the construction of high frequency approximate solutions. Preliminary numerical simulations that support these theoretical results are also reported.     

Heat equation and its comparative solutions

In this paper we will conduct an analytic comparative study between the powerful Adomian method and the traditional separation of variables method. This is achieved by handling homogeneous and non-homogeneous boundary value problem for one-dimensional heat equation. The study shows the reliability and efficiency of Adomian method. Adomian method provides the solution in a rapidly convergent series through evaluating elegantly computable components.     

Legendre spectral method for solving integral and integro-differential equations

A new spectral approximation of an integral based on Legendre approximation at the zeros of the first term of the residual is presented. The method is used to solve integral and integro-differential equations. The method generates approximations to the lower order derivatives of the function through successive integrations of the Legendre polynomial approximation to the highest order derivative. Numerical results are included to confirm the efficiency and accuracy of the method.     

Some minimum configuration L-stable rosenbrock methods with error estimators

Rosenbrock methods are a class of methods for solving ordinary differential equations. Minimum configuration methods are those which require a minimum amount of computational work per step. Minimum configuration Rosenbrock methods of orders 1, 2, 3 and 4 are described, together with error estimators which utilise imbedded processes of lower order. These error estimators require little additional work. The methods are all suitable for non-autonomous ordinary differential equations, and are L-stable.     

Numerical Solutions of a Nonlinear Evolution System with Small Dissipation on Parallel Processors

A nonlinear evolution system constructed from the Lorenz system is solved numerically by a parallelized predictor-corrector method. The numerical solution of such system reveals the details of interactions between dissipation and ellipticity and it may lead to better understanding of instability in some physical systems. Our algorithm and its implementation for solving this system is of general use for the study of strictly nonlinear parabolic equations.