Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method

Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.

A Probabilistic Method for Motion Analysis of Caisson Breakwaters

It is assumed that, during the design period, the waves acting on breakwaters are divided into three types： standing wave, broken wave and breaking wave,and the wave heights fit the Rayleigh distribution while the water depths, wave periods and duration of breaking wave impact force fit normal distribution. Based on the random samples of water depths, wave heights, wave periods and duration of breaking wave impact force, the types of waves acting on breakwaters are distinguished and the time-history model of the wave force is determined. The motions of caisson breakwaters under the wave force are simulated by a dynamic numerical model and the statistic characteristics of the dynamic responses are analyzed with the Monte Carlo method. A probabilistic procedure to analyze the motion of the breakwater is developed therein. The procedure is illustrated by an example.

Poisson theory and integration method for a dynamical system of relative motion

This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if （2n-1） first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.

Generation methodology of isolines of earthquake ground motion

Due to limited financial resources and challenging geographical conditions, the number of seismic observation networks in China is still very small and they are not widely distributed. Therefore, the available earthquake records obtained after an earthquake have been limited. In this paper, auto-generation methods to obtain strong motion isolines under different conditions are proposed. To verify the accuracy of these methods, some examples, including application to the 2008 Wenchuan earthquake, are given.

Synchronization motions of a two-link mechanism with an improved OPCL method

An improved OPCL method is developed and applied to both small swing and giant rotation synchronization of a two-link mechanism. Transition processes of the two kinds of synchronization are discussed. Comparisons of different motion characteristics of the two-link synchronization and the effects of different control parameters on synchronous processes are investigated with numerical simulations.

PLANNING MOTION TRACE OF ROBOT BY SPINOR METHOD

The spinors applied to describe position and attitude of robot are studied. In dual spaces, the terminal trace of robot is planned through the mapping point, of attitude spinors. As a handy method directly perceived through the sense, the spinor method directly converges tracking error in the planning. It promotes the dynamic accuracy of trace operation. It is also suitable to the exerciser with redundant freedom.

Underdetermined direction of arrival estimation with nonuniform linear motion sampling based on a small unmanned aerial vehicle platform

Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.

OPTIMAL MOTION PLANNING FOR A RIGID SPACECRAFT WITH TWO MOMENTUM WHEELS USING QUASI-NEWTON METHOD

An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors and the constraints on states. The motion planning for determining control inputs to minimize the cost functional is formulated as a nonlinear optimal control problem. Using the control parametrization, one can transform the infinite dimensional optimal control problem to a finite dimensional one that is solved via the quasi-Newton methods for a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planning scheme was applied to a rigid spacecraft with two momentum wheels. The simulation results show the effectiveness of the proposed optimal motion planning scheme.

Analysis on effect of surface fault to site ground motion using finite element method

Dynamic contact theory is applied to simulate the sliding of surface fault. Finite element method is used to analyze the effect of surface fault to site ground motions. Calculated results indicate that amplification effect is obvious in the area near surface fault, especially on the site that is in the downside fault. The results show that the effect of surface fault should be considered when important structure is constructed in the site with surface fault.

A TENSOR ANALYSIS METHOD FOR ESTIMATING 3-D MOTION PARAMETERS

By using the center projection image sequence to estimate 3-D motion parameters,one needs to know the corresponding relationship between the feature of motion object in spaceand the projection coordinate on image plane.In order to avoid using the relationship of featurecorrespondence,the tensor analysis method in the affine transformation system is presented,andthe simulation data of experimental results are given.

Experimental validation method of elastic thin rod model for simulating the motional cable harness

To analyze the spring disturbance torque caused by motionai cable harness in a stabilized platform, the Kirchhoff theory based cable harness model has been previously developed to dynamically simulate the motional cable harness. In this paper, this model was validated by comparing the simulation results with the experiment results （ both the spring force and the deformed profile of the motional cable harness）. In the experiment, a special optical measuring instrument based on binocular vision was developed and the motion and deformation of cable harness were measured. A simpli- fied stabilized platform system was constructed, and the absolute value of spring disturbance force during the motion of this simplified frame was obtained by using a force gauge （0. 02 N precision）. The physical parameters of experimental specimen were also measured. The experimental and simulated results showed good agreement. These results should be useful for better motional cable harness layout design and reliable evaluation of the spring disturbance torque.

A FIELD METHOD FOR INTEGRATING THE EQUATIONS OF MOTION OF NONHOLONOMIC CONTROLLABLE SYSTEMS

This paper presents a field method for integrating the equations of motion of nonholonomic controllable systems. An example is given to illustrate the application of the method.

Numerical Simulation of the Motion of A Floating Body with Partially Filled Tanks by A Pressure-Convection Particle Method

The moving particle semi-implicit（MPS）method has demonstrated its usefulness in practical engineering applications.Although it has wide applicability,it is still hard to predict the pressure precisely using the MPS method.A pressure-convection particle method based on the MPS method is proposed to overcome this problem.The improved performance of this new method is validated with computational and measured results.The approach is also applied to compute the problem of sloshing associated with floating body motion in waves.The pressure-convection MPS method demonstrated its capability to improve the prediction of pressure.

AN ANALYSIS OF AND APPROACH TO THE METHOD FOR TESTING THE PARALLELISM OF SAW GUIDE MOTION LOCUS AGAINST THE BLADE

The parallelism of saw guide motion locus against the blade is one of the main iterns in the testing of the geometric precision of the whole woodworking band saxving-machine. It reflects the making and mounting precisions of the sawguide device,having a direct effect on the working performance. the saw timber quality. and the safety (nature) of the woodworking band sawing-machine, so it is of great importance in the testing process of the band sawing-machine assembly and their going out of the plant.

Amended influence matrix method for removal of rigid motion in the interior BVP for plane elasticity

A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation （BIE） is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method. With this method, for the Neumann boundary value problem （BVP） of an interior region, a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.

A Method for Calculation of Low-Frequency Slow Drift Motions Based on NURBS for Floating Bodies

Through a higher-order boundary element method based on NURBS （Non-uniform Rational B-splines）, the calculation of second-order low-frequency forces and slow drift motions is conducted for floating bodies. In the floating body＇s inner domain, an auxiliary equation is obtained by applying a Green function which satisfies the solid surface condition. Then, the auxiliary equation and the velocity potential equation are combined in the fluid domain to remove the solid angle coefficient and the singularity of the double layer potentials in the integral equation. Thus, a new velocity potential integral equation is obtained. The new equation is extended to the inner domain to reheve the irregular frequency effects; on the basis of the order analysis, the comparison is made about the contribution of all integral terms with the result in the second-order tow-frequency problem; the higher-order boundary element method based on NURBS is apphed to calculate the geometric position and velocity potentials; the slow drift motions are calculated by the spectrum analysis method. Removing the solid angle coefficient can apply NURBS technology to the hydrodynamic calculation of floating bodies with complex surfaces, and the extended boundary integral method can reduce the irregular frequency effects. Order analysis shows that free surface integral can be neglected, and the numerical results can also prove the correctness of order analysis. The results of second-order low-frequency forces and slow drift motions and the comparison with the results from references show that the application of the NURBS technology to the second-order low-frequency problem is of high efficiency and credible results.

Zeno and the Wrong Understanding of Motion—A Philosophical-Mathematical Inquiry into the Concept of Finitude as a Peculiarity of Infinity

In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .

平面六杆机构运动特性的解析算法及COSMOSMotion仿真

本文先用解析法建立六杆机构运动特性的数学模型,利用Excel求出曲柄在不同位置时,导杆的运动变化情况。然后基于COSMOSMotion的运动仿真,绘出导杆的运动曲线,并将解析法计算值与仿真结果进行比较,以验证解析法数学模型的正确性。最后对仿真误差的来源进行了分析。

基于S-Method分布的微多普勒特征分析

微多普勒特征是雷达目标所具有的独特特征之一,对目标的分类、识别具有特殊的意义。研究高精度时频分析方法在分析目标微动特性中的作用,可以为后续目标识别提供很好的支撑。S-Method分布作为一种新型的时频分析方法,它基于短时傅里叶变换来实现,减少了分析过程中的运算量,同时能较好地解决交叉项问题。首先对弹道导弹弹头的微动模型进行建模,推导得到微动模型的理论微多普勒频率,然后采用S-Method分布对回波信号进行时频分析仿真实验,获得弹头目标章动的高精度的时间-微多普勒频率图。通过比较其在分析过程中的时频分辨率、交叉项,具体阐述S-Method分布在时频分析中的优势。因此可以将S-Method分布应用于雷达目标微多普勒分析中,分析实时变化的微多普勒频率特征。

Maxsurf Motions模块在船舶耐波性上的应用与验证

船舶作为海洋中最主要的运动物体,其在海浪中的运动问题,是船舶适航性、耐波性的基础,同时也是船舶设计建造中的关键步骤。采用Maxsurf Motions模块对4种国际标准船模进行了耐波性计算,验证了Maxsurf Motions中的切片理论和面元法的计算精度与可靠性,探讨了Motions程序在船舶耐波性分析中的可行性,分析了Motions模块计算误差的原因。结果表明:Motions模块对船舶运动响应以及波浪增阻的计算精度基本令人满意。对于附加质量系数和阻尼系数,Motions在中高频波段的计算精度较高。研究成果对Maxsurf Motions的应用起到一定的借鉴和指导作用,同时也提供了一系列耐波性计算的验证算例。