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euler equation
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  欧拉方程
     Aiming at the problem of multibody system difficult expression using bond graph, Chapter four systemically promotes the bond graph expression methods of complex mechanical system based on Euler equation of Newtonian mechanics, Lagrange equations of the first kind and Lagrange equations of the second kind.
     第四章针对键合图难于表达的多体动力学问题,系统地给出了基于牛顿力学的欧拉方程、第一类拉格朗日方程和第二类拉格朗日方程的复杂机械系统的键合图表达方法,给出了向量键合图的概念,并建立了多体动力学向量键合图的表达的详细方法和步骤,以解决多领域复杂系统的基于键合图的一体化建模问题。
短句来源
     From Euler equation to Einstein gravitational field equation
     从欧拉方程到爱因斯坦引力场方程(英文)
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     The Application of the Dual-euler Method for Overcoming the Singularity of Euler Equation in Parachute-Missile System
     双欧法在克服伞-弹系统欧拉方程奇异性中的应用
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     Study of the Application of Quaternions to Euler Equation
     四元数在欧拉方程中的应用研究
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     The NS solver is developed from Euler equation code by adding viscous terms and two-equation turbulence models.
     本文是在欧拉方程求解器的基础上,通过加入粘性(耗散)项,把流场的主控方程由欧拉方程(Euler)改为NS方程,然后引入两方程湍流模型,使其封闭。
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  euler方程
     The Axisymmetric H 1(R 3) Solution for 3 D Incompressible Euler Equation
     三维不可压缩Euler方程的H1(R~3)轴对称解
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     Oscilation and application of the Euler equation
     Euler方程的振动性及应用
短句来源
     Euler equation of weakly harmonic maps from high dimension Riemann manifold to homogeneous space
     高维Riemann流形到齐次空间弱调和映射的Euler方程
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     The stabilities about Navier-Stokes equation and Euler equation were brought into comparison;
     比较了Navier-Stokes方程和Euler方程的稳定性;
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     A Class of Upwind ENO Methods of Lines with Applications of Systems of Euler Equation
     一类逆风ENO线方法的构造及其对Euler方程的应用
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  euler公式
     In this paper, the active vibration control system of a 3 Dimensional supporter is realized based on smart structures. The finite element control equations are derived from Hamilton principle and Euler equation. The experimental results are provided.
     通过机敏结构建立了三维支撑结构的振动主动控制系统,利用Hamilton原理和变分法中的Euler公式导出了压电机敏结构的离散控制方程,采用加速度反馈实现了支架的振动主动控制
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     The technique proposed builds the sound field separation formula in wave number domain according to the superposition of particle velocity theorem and Euler equation in wave number domain, then the sound pressure caused by sources on one side of holographic plane can be obtained as expected by talcing inverse two-dimensional Fourier transform of this formula.
     提出的声场分离技术,利用全息面上微粒法向振速的叠加原理和波数域的Euler公式,建立起在波数域内的声场分离公式,然后通过二维逆Fourier变换,便得到了全息面一侧声源所产生的声压,从而达到声场分离的目的。
短句来源
     The formula of the sound field separation technique based on measurement of the three-dimensional acoustic intensity with single holographic plane was established according to the superposition theory of particle velocity and the Euler equation in wave number domain, and the acoustic pressure caused by the sound sources on one side of holographic plane was also obtained.
     根据全息面上微粒法向振速的叠加原理和波数域的 Euler公式,推导出基于单全息面三维声强测量的声场分离公式,将全息面两侧声源各自在全息面上产生的声压分离开来。
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  “euler equation”译为未确定词的双语例句
     To the lowest-order approximation in h, an important relation between the vacuum expectation value of color gauge fields and scalar fields is also derived by solving the Euler equation for the gauge fields.
     其次,在树图近似下,推导出了关于色规范场的真空期待值与标量场的真空期待值之间的一个重要关系式,并在此关系式的基础上,通过求解标量场的解而间接地给出了色规范场的解。
短句来源
     If u ∈ H_T is a solution of the corresponding Euler equation φ'±(u) = 0, u is a T—periodic solution of
     其中,H_T={u:Z→R~N|u(t+T)=u(t),t∈Z},而且其上的内积为
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     Comparative Coefficient Ways in Resolving Special Type Non-homogeneous Euler Equation
     特殊类型的欧拉非齐方程的比较系数法
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     Numerical Comparison of the Second-order Godunov Scheme MUSCL and the Fifth-order FD-WENO Scheme for Compressible Euler Equation
     五阶FD-WENO格式与二阶Godunov格式MUSCL的数值测试与比较
短句来源
     2. The C∞stability of Euler equation determines C∞stability of some models when viscosity (molecule viscosity、turbulent viscosity) is neglected during atmospheric motion.
     2. Euler方程组的C∞稳定性决定了大气运动不考虑粘性(分子粘性、湍流摩擦)时的众多模式的C∞稳定性。
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  euler equation
At large Reynolds numbers, the problem of determining the pressure distribution comes down to solving the Euler equation with corresponding boundary conditions.
      
The fluid is assumed to be ideal and incompressible and its flow symmetric; the lateral bending of the beam is described by the Euler equation.
      
The singularities of the corresponding analog of the Jacobi equation (and of the Euler equation) are generated by the procedure of integration by parts, which leads to differentiation with respect to measures glued (joined) together.
      
These relationships are based on the Euler equation, the correspondence principle, and the rule of contiguity of regions.
      
The Euler equation for the energy functional leads to a second-order differential equation for the canonical profile of the function μ = 1/q.
      
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To be able to locate the point of inception of air entrainment is of considerable significance in the design of ski-jump spillways for high dams, in that this is not only prerequisite to the theoretical analysis of jet diffusion in the air and the subsequent alleviation of erosion as the aerated jet dives to the bed, but also essential if the possible benefit of aeration in the reduction of concrete pitting is to be evaluated. Although past contributions to this problem are numerous, no method has yet been available...

To be able to locate the point of inception of air entrainment is of considerable significance in the design of ski-jump spillways for high dams, in that this is not only prerequisite to the theoretical analysis of jet diffusion in the air and the subsequent alleviation of erosion as the aerated jet dives to the bed, but also essential if the possible benefit of aeration in the reduction of concrete pitting is to be evaluated. Although past contributions to this problem are numerous, no method has yet been available to yield the correct prediction of the onset of aeration in or downstream of the curvilinear portion of the spillway which is known to take place much earlier than usual. Even for the straight portion of the spillway, calculated positions of aeration inception do not always match with the observed values (see table 1, and compare columns 4 to 7). In this paper is presented a rational and yet rather simple procedure with which one may treat the general problem of locating the position of aeration inception no matter if the spillway contains a curve or not. In the first place, the irrotational or "ambient" flow outside of the boundary layer is studied. In view of the fact that the flow over the spillway of a high dam is much smaller in extent laterally than longitudinally, an approximation similar to that used in the derivation of boundary layer equations from the Navier-Stokes equations is applied to the Euler equations. The resulting expressions indicate that the usual assumption of concentric streamlines is justifiable. The depth of flow is taken as that so calculated plus the displacement thickness of the boundary layer. Since on the plane of the complex potential, the flow over a spillway may be formulated as a simply-mixed boundaryvalue problem, Wood's exact method is applied to a numerical example with gravitational effect taken into consideration. The result of calculation indicates that both methods yield practically the same depth of flow. The inception of aeration is, as usual, assumed to occur as the boundary layer meets the free surface. Under the combined influence of gravity and boundary geometry, the flow over a dam is continuously accelerated or decelerated. In such case, boundary-layer computation by usual method is both involved and of doubtful accuracy. It is found, however, that in the case of flow over a spillway, the flow outside of the turbulent boundary layer conforms to a condition of self-preservation as proposed by Townsend. Since the Reynolds number for high dams may surely reach very high values, the turbulent boundary layer itself may be assumed to be approximately self-preserving. In short, this means that Townsend's theory of approximate self-preservation for boundary layers under the influence of longitudinal acceleration may be applied. This also means that the computation of boundary layer development may be much simplified. Based on an analysis of prototype data, it is found that in the present case involving air-entrainment inception, thickness of the boundary layer should be defined as that at which the mean velocity is within 0.1% of the velocity of flow outside the boundary layer. In the carrying out of the computations, boundary layer thickness at various sections are first estimated, then the irrotational flow outside the boundary layer is analysed by the simplified method to obtain the surface profile and the parameter "a" denoting the variation of velocity along the surface, and finally Townsend's theory of approximate self-preservation is applied to recompute the thickness of the boundary layer along the spillway. As any error made in the estimation of boundary-layer thickness has little effect on the computation of surface profile and hence on any subsequent computations, reasonably experienced computers should find it unnecessary to repeat the computations. Results of computations are found to be within 10% of the observed data obtained at two dams.

鉴于现有掺气发生点的计算方法误差可达观测值的70%以上,本文根据原型掺气发生点观测资料探讨较准确的计算方法,在无特殊干扰的条件下,掺气的发生取决于紊流边界层的发展.坝面边界层流动的特点是:雷诺数高(u_1x/,v在10~8至10~(10)之间),坝面粗糙,和水流先加速后减速因而纵向流速梯度对边界层发展的影响必须考虑.针对这些特点和坝面及陡槽高速水流具有自模性质,本文建议应用自模理论进行计算.计算的掺气点位置与实测位置比较误差减至10%左右,从而为掺气发生点或坝面紊流边界层的计算提供了较可靠的方法.

In the free-boundary case, the extremum of the potential functional is found from the variational principle. Thereby the equation and boundary conditions required for plasma equilibrium are derived. The Euler equation of the relevant functional is the magnetic surface function equation with the condition of free boundary. A variational functional suitable for numerical computation is given. This functional corresponds to a boundary value problem with an equal-value surface boundary condition....

In the free-boundary case, the extremum of the potential functional is found from the variational principle. Thereby the equation and boundary conditions required for plasma equilibrium are derived. The Euler equation of the relevant functional is the magnetic surface function equation with the condition of free boundary. A variational functional suitable for numerical computation is given. This functional corresponds to a boundary value problem with an equal-value surface boundary condition. For the case of a conducting wall of simple geometry (i.e., a rectangular wall), numerical computation has been carried out by using the Ritz method.

在自由界面情况下用求位能汛函极值的变分原理推出了等离子体平衡所需满足的平衡方程和边界条件;其泛函的Euler方程即为具有自由界面条件的磁面函数方程。也给出了便于计算的变分泛函,它相当于等值面边界问题。对于导体壁为简单几何形状的情况,用Rit法进行了数值计算。

This paper uses the variational method to calculate the configurations of projectile nose with the minimum drag under the conditions that the sum of nose wave resistance and frictional resistance satisfies the extremes (Euler equation). This paper also analyses and computes numerically the optimum nose L/D (length-to-diameter ratio), secant parabolic nose and tail contraction ratio and presents the calculated curve.

本文通过变分法,在同时考虑弹体头部波阻、摩擦阻力二音之和满足其极值条件(欧拉方程)时,得到了最小阻力的头部外形。并对最佳头部长细比、相割抛物线形头部、最佳尾部收缩比进行了数值分析计算,给出了计算曲线。

 
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