D''Alembeft定理中的旋转轴和旋转角度

一般运动分解为先平移，求得二重点之后，再旋转；通过对空间及矩阵秩的分析，证明了旋转轴的惟一性。并对射影几何中文字描述的达兰倍尔定理^[1]建立了解析表达式，给出了过二重点的旋转轴方位和旋转角度的计算公式，使得二个同向不重合的合同形体经过一次旋转达到重合；具有既可以图解，又能精确计算的特点。     

Distribution of the displacement sequence of an orientation preserving circle homeomorphism

In some applications not only the knowledge of the behaviour of trajectories of a map is important, but also their displacements. We describe in detail the distribution of elements of the displacement sequence along a trajectory of an orientation preserving circle homeomorphism ? with irrational rotation number ?(?). The values of displacement are dense in a set which depends on the map γ (semi-)conjugating ? with the rotation by ?(?) and which is the support of the displacement distribution. We provide an effective formula for the density of this distribution if γ is a C¹-diffeomorphism. Moreover, we show approximation of the displacement distribution by sample displacements measured for any other circle homeomorphism sufficiently close to the initial homeomorphism ?, which constitutes a rigorous proof of numerical results seen in certain integrate-and-fire models.     

A new Leapfrog scheme for rotational motion in 3D

Discrete element codes use complex geometric solid particles, so it is necessary to integrate three‐dimensional rigid‐body rotation correctly with external torque. This article presents an interpretation of the Leapfrog scheme. We begin with some rotation formulae before presenting an efficient and high‐order recurrent Taylor series method for rotation. Integrating this method with Leapfrog interpretation provides a complete scheme for rotational motion with external torque. This new Leapfrog scheme has been integrated into the CeaMka3D Discrete Element code, and we present some verifications and simulations to illustrate the capabilities of this scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Rotation manifold <Emphasis Type="Italic">SO</Emphasis>(3) and its tangential vectors

In this paper, we prove that incremental material rotation vectors belong to different tangent spaces of the rotation manifold SO(3) at a different instant. Moreover, we show that the material tangent space as the tangent space at unity is not a possible definition yielding geometrically inconsistent results, although this kind of definition is widely adopted in applied mechanics community. In addition, we show that the standard Newmark integration scheme for incremental rotations neglects first order terms of rotation vector, not third order terms. Finally, we show that the rotation interpolation of extracted nodal values on the rotation manifold is not an objective interpolation under the observer transformation. This clarifies controversy about the frame-indifference of geometrically exact beam formulations in their finite element implementations.     

On piecewise smoothness of conjugacy of class P circle homeomorphisms to diffeomorphisms and rotations

We give a characterization of piecewise C ¹ class P-homeomorphism f of the circle with irrational rotation number and finitely many break points which is piecewise C ¹ conjugate to a C ¹-diffeomorphism. The following properties are equivalent:

?(i)?f is conjugate to a C ¹-diffeomorphism of the circle by a piecewise C ¹-homeomorphism. (ii)?The product of jumps of f in the break points contained in a same orbit is trivial. (iii)?f is conjugate to a C ¹-diffeomorphism of the circle by a piecewise linear (PL)-homeomorphism or a piecewise quadratic homeomorphism.

For a PL-homeomorphism f having the property (ii): f is conjugate to a rotation either by a PL-homeomorphism or by a piecewise analytic homeomorphism.     

转轴轴线可变的2T1R并联机构运动模式分析

目的设计一种可调整包装件姿态的分拣、装箱的并联机器人构型。方法使用位移流形理论综合具有2T1R运动模式的并联机构。用旋量理论分析这种新型机构在一般位形下运动模式的自由度特征,并分析其支链驱动副选取的可行性。结果这种新型并联机构能实现具有转动轴线方向可变的2T1R运动模式。结论该机构具有的运动模式与设计预期相符,可进行平面的移动和转动轴线变化的一维球面转动。复杂形状的产品在装箱、分拣时,可能需要调整产品的空间姿态,具有转动轴线可变的2T1R运动模式的并联机构,可在该工况下进行应用。     

Total Lagrangian Reissner's geometrically exact beam element without singularities

In this paper, we introduce a new Reissner's geometrically exact beam element, which is based on a total Lagrangian updating procedure. The element has the rotation vector as the dependent variable and the singularity problems at the rotation angle 2π and its multiples are passed by the change of parametrization on the rotation manifold. The beam formulation has several benefits such as all the unknown vectors belong to the same tangential vector space, no need for secondary storage variables, the path‐independence in the static case, any standard time‐integration algorithm may be used, and the symmetric stiffness. Copyright © 2006 John Wiley & Sons, Ltd.     

自适应Chirplet信号分解用于ISAR目标三维转动检测

当ISAR目标作复杂的三维转动时,目标上各散射点的相位误差将与它们在目标上所处的位置有关,传统的相位聚焦方法难以采用统一的相位校正函数来进行补偿。为解决此问题,论文提出了一种基于自适应Chirplet信号分解的ISAR目标三维转动检测方法,该方法使用自适应Chirplet信号分解的快速算法来估计散射点子回波的相位信息,并根据两个散射点相位之间的非线性度来判断目标是否存在三维转动,从而只选择那些仅具有二维转动的数据段进行成像。仿真实验结果表明了它的有效性。     

Precession Vibrations of the Two-Blade Rotor with the Elastic Weightless Shaft in Compound Rotation

The problem of precession vibrations of the rigid two-blade rotor with the elastic weightless shaft in compound rotation, when its axis executes an additional forced slew, was stated. The equations of vibrations of the system were derived, their periodic solutions for the case of steady motion were found at different values of the angular velocity of its own rotation. The resonance value of this velocity was determined, the amplitude-frequency characteristics in the pre- and postresonance states were plotted.     

Limit sets of convex non-elastic billiards

Inspired by the work of Pujals and Sambarino on dominated splitting [E.R. Pujals and M. Sambarino, On the dynamics of dominated splitting, Ann. Math. 169 (2009), pp. 675–740], we present billiards with a modified reflection law which constitute simple examples of dynamical systems with limit sets having dominated splitting and where the dynamics is a rational or irrational rotation.     

Some Results of the Educational Experiment APIS (Cervantes Mission on Board ISS)

Some results of the analysis of the pictures taken along the performance of the Análisis de Propiedades Inerciales de Sólidos, Analysis of the Inertia Properties of Solid Bodies (APIS) experiment carried out in the Cervantes mission on board ISS, are presented. APIS was an educational experiment devoted to take advantage of the unique conditions of absence of relative gravity forces of a space platform such as ISS, to show some of the characteristics of the free rotational motion of a solid body, which are impossible to carry out on earth. This field of experimental research has application to aerospace engineering science (e.g. attitude control of spacecrafts), to astrophysical sciences (e.g. state of rotation and tumbling motions of asteroids) and to engineering education. To avoid the effect of the ambient atmosphere loads on the motion, the test body is placed inside a sphere, which reduces the effect of the aerodynamic forces to just friction. The drastic reduction of the effect of the surrounding air during the short duration of the experimental sequences allows us to compare the actual motion with the known solutions for the solid body rotation in vacuum. In this paper, some selected, relevant sequences of the sphere enclosing a body with a nominal cylindrical inertia tensor, put into rotation by the astronaut, are shown; the main problems to extract the information concerning the characteristic parameters of the motion are outlined, and some of the results obtained concerning the motion of the test probe are included, which show what seems to be a curious and unexpected solution of the Euler equations for the solid body rotation in vacuum, without energy dissipation, when the angular momentum is almost perpendicular to the axisymmetry axis.     

Medium resolution magneto-optical Faraday rotation measurement system

Medium resolution magneto-optic Faraday rotation measurement setup has been reported. Measuremental setup reported is made up of simple polarized laser source, beam expander, analyzer and a bisected cross polarizedp-n detector for single ended measurements. Result of CoO modified yttrium iron garnet (YIG) films showed a rotation of 3 deg/μm which is comparable to earlier reported Co-doped YIG films. Paper presented at the poster session of MRSI AGM VI, Kharagpur, 1995     

高转速FSW工艺特征及焊缝组织性能演变规律研究

目的研究不同转速的焊缝性能变化对组织的影响,以期为高转速搅拌摩擦焊工艺参数的优化和更大范围的应用提供指导。方法在3000~8000 r/min的高转速范围内对3A21-O态铝合金进行搅拌摩擦焊试验,焊后分析了焊缝成形特征和晶粒形态并测试了接头截面显微硬度。结果当转速由1000~4000 r/min区间升高至5000~8000 r/min区间时,焊核宽度急剧增大了近50%。这是由于焊具产热机制以滑移摩擦为主向以粘着摩擦为主转变,导致上述焊核宽度增大的行为。随着转速的增大,焊缝温度呈现出常规搅拌摩擦焊工艺中鲜见的先增大而后趋于稳定的变化趋势;温度随转速的这一演变特征导致焊缝焊核区的亚结构数量比例以及显微硬度都随转速呈现出与此相近的演变规律。结论在高转速搅拌摩擦焊中,转速提高能提高焊缝性能,且增强的焊缝性能能够在较宽的高转速区间内保持相对稳定的状态。     

The unique ergodic measure of the symmetric piecewise toral isometry of rotation angle θ=kπ/5 is the Hausdorff measure of its singular set

It is known that the symmetric piecewise toral isometry of rotation angle θ = k π /5, k=1, 2, 3, 4 is uniquely ergodic in 'a certain subset' of its singular set (aka exceptional set). The purpose of this paper is to identify the unique ergodic measure explicitly. In fact, we prove that the unique ergodic measure is none other than the normalized Hausdorff measure of the singular set, consequently proving that the unique ergodicity holds in the entire singular set. We use the 'phantom dynamics' given by a number of symmetry identifications as our main tool.     

Oscillation behavior of a high-temperature silicon droplet by the electromagnetic levitation technique superimposed with a static magnetic field

When a static magnetic field was applied to a Si droplet levitated by an electromagnetic force, only one peak was observed to remain in the frequency spectrum. It was the objective of this work to clarify whether this peak can be assigned to the m = ± 2 oscillation or to the rotation of the droplet. By analyzing the behavior of the deflection angle of the droplet in a top view, we conclude that this peak is not due to the surface oscillation of the droplet but to the droplet rotation.     

Metal plasticity by grain rotation—Microdiffraction case studies

The synchrotron-based X-ray Laue microdiffraction technique has become more and more popular over that last year. In addition to measuring the deviatoric part of the elastic strain tensor this technique is specifically accurate in measuring grain rotations. The current paper illustrates the high rotational sensitivity by three deformation mechanisms that lead to grain rotation; one mechanism is the nearly diffusionless interaction between disclinations and dislocations a mechanism for low homologous temperatures and two mechanisms are interactions between diffusive mechanisms and dislocation motion, namely hillock growth upon thermal cycling and during electromigration. The communalities and differences between these mechanisms are discussed to provide further insight into a special deformation mode.     

Strongly orthotropic continuum mechanics and finite element treatment

Despite successful application to orthotropic analysis, any Lagrangian strain tensor that is symmetric can be classified as an isotropic metric, while the infinitely orthotropic case can be accurately dealt with using one‐dimensional elements, structural tensors or kinematic constraints. In this paper, we present a strongly orthotropic continuum mechanics basis that models the exact kinematic behavior of the intermediary class of materials and also show its application to multi‐axial media and treatment using the finite element method. By asserting that mechanistic strain metrics must be material property dependent and satisfy equilibrium, we are able to derive a novel orthotropic linear strain tensor that is asymmetric and thus capable of describing all levels of orthotropy, while maintaining generality to the well‐established isotropic approach. Subsequently formulated are a material principal rotation tensor, extended orthotropic compliance tensor and an extended Mohr's plot for strain relying on an additional metric denoted as aspectual strain. Using the developed finite element formulation, it is shown that identical stress results to conventional theory for an orthotropic linear problem are predicted, while offering a more informative analysis. A second numerical example demonstrates the unique capability of this approach to solve the erroneous response of strongly orthotropic materials under trellis shear as compared with a number of conventional and contemporary approaches and thus its ability to produce kinematically exact results. Copyright © 2008 John Wiley & Sons, Ltd.     

Propagation of a Thermoelastic Wave in a Half-Space of a Homogeneous Isotropic Material Subjected to the Effect of Rotation and Initial Stress

The propagation of thermoelastic waves in a homogeneous, isotropic elastic semi-infinite space is subjected to rotation and initial stress, which is at temperature T₀ - initially, and whose boundary surface is subjected to heat source and load moving with finite velocity. Temperature and stress distribution occurring due to heating or cooling and have been determined using certain boundary conditions. Numerical results have been given and illustrated graphically in each case considered. Comparison is made with the results predicted by the theory of thermoelasticity in the absence of rotation and initial stress. The results indicate that the effect of the rotation and initial stress is very pronounced.     

含转动干扰粘性阻尼墙的阻尼特性试验研究

通过粘性阻尼墙的非线性动力学试验建立阻尼参数力学模型，研究阻尼参数在具有旋转运动剪切模式的非线性特性及随振动幅值和振动频率的变化规律，给出了适合工程应用参考经验拟合公式，研究显示粘性阻尼墙在剪切模式下可提供高层建筑较大的阻尼特性，旋转运动对阻尼常数有较大的影响，研究结果可以为工程应用提供参考。可为高层建筑抵制地震和风振提供有效的动力学设计手段。     

Symmetric and non-symmetric periodic orbits for the digital filter map

We exhibit instances of non-symmetric periodic orbits for the digital filter map, resolving a question posed in the literature as to whether such orbits can exist. This piecewise irrational rotation, depending on a parameter a = 2cos θ, is an isometry of [?1, 1) × [?1, 1) and reflections in the two diagonals are time-reversing symmetries for the map. Symmetric orbits are plentiful and have been much investigated. Each periodic orbit is paired with a symbolic string, from the alphabet {?, 0, +}, arising under iteration of the map because of the presence of a line of discontinuity. We prove the existence of an infinite family of non-symmetric orbits where the period N starts at 29 and increases in steps of 5; they correspond to the strings (+00)⁵(+?)² 0 ^N?19. We describe several computer algorithms to find non-symmetric periodic orbits and their symbolic strings and list non-symmetric strings both for a = 0.5, and for N ≤ 100 across the parameter range. Our evidence suggests that non-symmetric orbits, though not plentiful, are characteristic of the dynamics of the map for all parameter values.