变分原理和非线性Lyapunov稳定性判据     

罗德海 《成都信息工程学院学报》1993,(4)

本文通过构造斜压大气运动的原始方程模式和两层模式的Hamilton守恒量及积分不变的Casimir泛函,并使用变分法,得到了斜压大气运动的非线性Lyapunov稳定性判据,这个判据是Arnold-Blumen-Zeng判据的推广。  相似文献   

传感器信号调制脉冲序列抽样频率的确定     

吴凡 《广东海洋大学学报》2003,23(1):51-56

通过对传感器输出信号波形有无振荡进行分类 ,依据传感器响应时间的定义 ,分别找到一阶、二阶及理想动态传感器的频带上限与动态响应时间两者间的关系式 ;提出了传感器“受激系数”的概念 ,推导出输出信号波形有无振荡两种传感器之间的比例关系。并通过一个数值例子 ,说明所推导出关系式的应用。  相似文献   

On Charged Analogues of Buchdahl’S Type Fluid Spheres     

Y.?K.?Gupta  Mukesh?KumarEmail author 《Astrophysics and Space Science》2005,299(1):43-59

In this article the charged analogues of recently derived Buchdahl’s type fluid spheres have been obtained by considering a particular form of electric field intensity. In this process, Einstein–Maxwell field equations yield eight different classes of solutions, joining smoothly with the exterior Reissner–Nordstrom metric at the pressure free intersurface. Out of the eight solutions only seven could be utilized to represent superdense star models with ultrahigh surface density of the order 2×10¹⁴ gm cm⁻³. The maximum masses of the star models were found to be 8.223931M_Θ and 8.460857M_Θ subject to strong and weak energy conditions, respectively, which are much higher than the maximum masses 3.82M_Θ and 4.57M_Θ allowed in the neutral cases. The velocity of sound seen to be less than that of light throughout the star models.  相似文献   

    

Michael W. D. Davis  Michel David  Jean-Marc Belisle 《Mathematical Geology》1978,10(4):369-374

In mineral deposit evaluation, the estimation of block values can involve the solution of as many as 100,000 systems of linear equations. To minimize computing costs it is important that the program to solve the linear systems be as efficient as possible. Standard library routines tend to contain very general stable methods using pivoting and iteration to ensure high accuracy solutions. Here, a particular method has been developed that gives a substantial improvement in run time at the occasional expense of accuracy and stability. The method is not new—just a simple application of Gaussian elimination in the symmetric case.  相似文献   

Stochastic Hill's equations for the study of errant rocket burns in orbit     

Martin Ostoja-Starzewski  James M. Longuski 《Celestial Mechanics and Dynamical Astronomy》1992,54(4):295-303

The problem of errant rocket burns in low Earth orbit is of growing interest, especially in the area of safety analysis of nuclear powered spacecraft. The development of stochastic Hill's equations provides a rigorous mathematical tool for the study of such errant rocket maneuvers. These equations are analyzed within the context of a theory of linear dynamical systems driven by a random white noise. It is established that the trajectories of an errant rocket are realizations of a Gauss-Markov process, whose mean vector is given by the solution of a deterministic rocket problem. The time-dependent covariance matrix of the process is derived in an explicit form.  相似文献   

Theory of Basin Scale Dynamics of a Stratified Rotating Fluid     

Leo R. M. Maas 《Surveys in Geophysics》2004,25(3-4):249-279

The dynamics of a stratified fluid contained in a rotating rectangular box is described in terms of the evolution of the lowest moments of its density and momentum fields. The first moment of the density field also gives the position of the fluids centre-of-mass. The resulting low-order model allows for fast assessment both of adopted parameterisations, as well as of particular values of parameters. In the ideal fluid limit (neglect of viscous and diffusive effects), in the absence of wind, the equations have a Hamiltonian structure that is integrable (non-integrable) in the absence (presence) of differential heating. In a non-rotating convective regime, dynamically rich behaviour and strong dependence on the single (lumped) parameter are established. For small values of this parameter, in a self-similar regime, further reduction to an explicit map is discussed in an Appendix. Introducing rotation in a nearly geostrophic regime leads through a Hopf bifurcation to a limit cycle, and under the influence of wind and salt to multiple equilibria and chaos, respectively.  相似文献   

Duality properties of Gorringe–Leach equations     

Yves Grandati  Alain Bérard  Hervé Mohrbach 《Celestial Mechanics and Dynamical Astronomy》2009,103(2):133-141

In the category of motions preserving the angular momentum direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold–Vassiliev type. The specific associated conserved quantities (Laplace–Runge–Lenz vector and Fradkin–Jauch–Hill tensor) are then dual reflections of each other.  相似文献   

Analytical solutions for the equations of motion of a space vehicle during the atmospheric re-entry phase on a 2-D trajectory     

Gabriel Mititelu 《Celestial Mechanics and Dynamical Astronomy》2009,103(4):327-342

A practical and important problem encountered during the atmospheric re-entry phase is to determine analytical solutions for the space vehicle dynamical equations of motion. The author proposes new solutions for the equations of trajectory and flight-path angle of the space vehicle during the re-entry phase in Earth’s atmosphere. Explicit analytical solutions for the aerodynamic equations of motion can be effectively applied to investigate and control the rocket flight characteristics. Setting the initial conditions for the speed, re-entering flight-path angle, altitude, atmosphere density, lift and drag coefficients, the nonlinear differential equations of motion are linearized by a proper choice of the re-entry range angles. After integration, the solutions are expressed with the Exponential Integral, and Generalized Exponential Integral functions. Theoretical frameworks for proposed solutions as well as, several numerical examples, are presented.  相似文献   

Solution of Lane-Emden type equations using Bernstein operational matrix of differentiation     

Rajesh K. Pandey  Narayan Kumar 《New Astronomy》2012,17(3):303-308

The purpose of this paper is to propose an efficient numerical method for solving Lane-Emden type equations arising in astrophysics using Bernstein polynomials. First Bernstein operational matrix of differentiation is derived using Bernstein polynomials and then applied to solve the linear and nonlinear differential equations of Lane-Emden type. Some illustrative examples are given to demonstrate the efficiency and validity of the proposed algorithm.  相似文献   

Lippmann-Schwinger积分方程广义超松弛迭代解法及其收敛特性          下载免费PDF全文

徐杨杨  孙建国  商耀达  孟祥羽  魏脯力 《地球物理学报》2021,64(1):249-262

为克服Born级数只适用于弱散射和短程传播的弱点,从光学散射理论中引入了针对强光学散射问题的Lippmann-Schwinger方程广义超松弛迭代解法,并对这种方法在反射地震条件下的算法表现、收敛特点、计算效率以及计算精度等问题进行了分析和讨论.理论分析和数值计算结果均表明:(1)与散射级数重整化相比,超松弛法具有更坚实的数学基础;(2)超松弛法可以有效地克服Born级数的弱点,得到与有限差分相当的数值模拟结果;(3)在反射地震条件下LS方程超松弛法表现优异,完全可以解决反射地震数值模拟中的强散射问题.  相似文献