共查询到18条相似文献,搜索用时 453 毫秒
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文章对非相对论下均匀斜交电磁场中的正电荷+q进行了动力学矢量分析,将其运动分解为沿磁场方向的匀加速直线运动、垂直于电、磁场方向的匀速直线运动和垂直于磁场方向的匀速率圆周运动,进而推理出电荷完整的运动学方程;然后将运动学方程进行"约化"和简化,作出不同初速度下电荷在xy平面内的投影运动轨迹并加以分析,指出轨迹的若干特点及... 相似文献
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欧拉运动学方程的推导,关键是确定本体坐标系与空间坐标系之间的转换关系.通过引进方位矢量可以较轻易地得到反映两坐标系转换关系的转换张量,从而能清晰直观地推导出欧拉运动学方程,而这是有别于传统的推导方法的. 相似文献
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对单摆法测液体黏度装置进行改进,利用图像传感器捕捉液体中摆球的运动轨迹,再采用图象分析软件Track提取其位置坐标,利用双平方权重法排除异常点,基于液体中小球运动学方程的动力学模型,对考虑了液体阻力的单摆运动方程进行求解,通过双平方权重的最小二乘法对动力学方程进行拟合,得到稳定的方程解,求出待测液体的黏度. 相似文献
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对有心力场中的行星轨迹问题,通过建立以复数矢量为变量的方程进行求解.在求解过程中不仅得到了行星运动的一般性规律,还推导出行星的速度公式和哈密顿定理,同时发现行星轨道的第二焦点位置及基于拉普拉斯-隆格-楞次矢量的轨迹方程,并由此求出不同方向发射卫星的轨迹包络线. 相似文献
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S. S. Stepanov 《Physics of Particles and Nuclei》2012,43(1):128-145
In this paper we obtain the differential equations which describe the rotating rod and precession of the spin of a gyroscope
moving along a curved trajectory. Several examples of such motion are considered. The obtained equations differ from the traditional
Thomas expression, interpreted as a rotation of the noninertial frame relative to the fixed one. The cause of this disagreement
is the fact that, in general, the axes of the moving frame are not orthogonal for the fixed observers. When the velocity changes,
the axes’ direction changes, due to both Wigner rotation and Lorentz contraction. In the present paper we take into account
both of these factors. It is shown that the vectors representing various physical quantities transform in different ways in
the moving reference frame. Thus, the kinematic equations describing the motion of these quantities in a fixed frame are different
as well. 相似文献
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由牛顿第二定律得到二维各向同性带电谐振子在均匀磁场中运动的运动微分方程,通过对运动微分方程的直接积分得到系统的两个积分(守恒量).利用Legendre变换建立守恒量与Lagrange函数间的关系,从而求得系统的Lagrange函数,并讨论与守恒量相应的无限小变换的Noether对称性与Lie对称性,最后求得系统的运动学方程. 相似文献
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A complete angular momentum analysis of the integral equations of motion for four identical spinless particles is given. After separation of the variables associated with rotation, the equations of motion take the form of an infinite set of coupled integral equations in three continuous variables. In general, the four-particle kinematic factors in the integral kernels are expressed as bilinear combinations of factors of the three-particle kinematic factors type. For the case of a separable two-particle interaction the equations obtained are simplified so that they are reduced to coupled integral equations in two continuous variables. 相似文献
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In this paper, the nonlinear forced vibration behavior of composite plates reinforced by carbon nanotubes is investigated by a numerical approach. The reinforcement is considered to be functionally graded (FG) in the thickness direction according to a micromechanical model. The first-order shear deformation theory and von Kármán-type kinematic relations are employed. The governing equations and the corresponding boundary conditions are derived with the use of Hamilton's principle. The generalized differential quadrature (GDQ) method is utilized to achieve a discretized set of nonlinear governing equations. A Galerkin-based scheme is then applied to obtain a time-varying set of ordinary differential equations of Duffing-type. Subsequently, a time periodic discretization is done and the frequency response of plates is determined via the pseudo-arc length continuation method. Selected numerical results are given for the effects of different parameters on the nonlinear forced vibration characteristics of uniformly distributed carbon nanotube- and FG carbon nanotube-reinforced composite plates. It is found that with the increase of CNT volume fraction, the flexural stiffness of plate increases; and hence its natural frequency gets larger. Moreover, it is observed that the distribution type of CNTs significantly affects the vibrational behavior of plate. The results also show that when the mid-plane of plate is CNT-rich, the natural frequency takes its minimum value and the hardening-type response of plate is intensified. 相似文献
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In this paper, vibration of a bladed unbalanced flexible rotor is studied. The blade that is attached to the disk is considered as a fixed-free Euler-Bernoulli beam. Position of the blade with respect to the eccentric mass is taken into consideration. Coupled equations of the motion of unbalanced rotor and the blades are obtained through Lagrange equations. The dynamic equations have time variant periodic coefficients. Transient vibration analysis showed that rotor acceleration excites the blade vibration with its own natural frequency. While the rotor passes through its own natural frequency (critical speed) the blade vibration is again excited but this time with the rotor natural frequency. Modal behavior of the blades are different for subcritical, supercritical and for critical speed of the rotor. In the subcritical run of the rotor, blades located from 0° to 180° with respect to the eccentric mass are deflected in the negative direction while the rest are deflected in the positive direction. For supercritical run of the rotor, modal behavior of the blades is just the opposite. For critical speed of the rotor, blades located 90° to 270° from the eccentric mass are deflected in the positive direction while the rest of the blades are deflected in the negative direction. Blades have also different deflections. When the deflections of the blades are plotted with respect to their position angle, distribution of the blade deflections has a sinusoidal shape. 相似文献
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J.-L. Guermond R. Laguerre J. Léorat C. Nore 《Journal of computational physics》2009,228(8):2739-2757
The Maxwell equations in the MHD limit in heterogeneous axisymmetric domains composed of conducting and non-conducting regions are solved by using a mixed Fourier/Lagrange finite element technique. Finite elements are used in the meridian plane and Fourier modes are used in the azimuthal direction. Parallelization is made with respect to the Fourier modes. Continuity conditions across interfaces are enforced using an interior penalty technique. The performance of the method is illustrated on kinematic and full dynamo configurations. 相似文献
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We study the nonlinear propagation of dust-ion acoustic (DIA) shock waves in an un-magnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev-Petviashivili-Burgers (K-P-Burgers) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the K-P-Burgers equation is obtained and its properties are analysed with different plasma number densities, ion temperatures and masses. It is shown that a transition from shocks with negative potential to positive one occurs depending on the negative ion concentration in the plasma and the obliqueness of propagation of DIA waves. 相似文献
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The main aim of this paper is to provide a simple yet efficient solution for the free vibration analysis of functionally graded (FG) conical shells and annular plates. A solution approach based on Haar wavelet is introduced and the first-order shear deformation shell theory is adopted to formulate the theoretical model. The material properties of the shells are assumed to vary continuously in the thickness direction according to general four-parameter power-law distributions in terms of volume fractions of the constituents. The separation of variables is first performed; then Haar wavelet discretization is applied with respect to the axial direction and Fourier series is assumed with respect to the circumferential direction. The constants appearing from the integrating process are determined by boundary conditions, and thus the partial differential equations are transformed into algebraic equations. Then natural frequencies of the FG shells are obtained by solving algebraic equations. Accuracy and reliability of the current method are validated by comparing the present results with the existing solutions. Effects of some geometrical and material parameters on the natural frequencies of shells are discussed and some selected mode shapes are given for illustrative purposes. It’s found that accurate frequencies can be obtained by using a small number of collocation points and boundary conditions can be easily achieved. The advantages of this current solution method consist in its simplicity, fast convergence and excellent accuracy. 相似文献