捷联惯导系统中的圆锥和伪圆锥运动研究

分别对圆锥运动和伪圆锥运动的产生原因、表达形式,以及对捷联惯导系统的影响进行了分析.由于圆锥运动和伪圆锥运动并不相同,因此圆锥运动补偿算法将对两者产生不同的效果.数字仿真表明,圆锥补偿算法可以大大降低经典圆锥运动对捷联导航系统的不利影响,但同时却会增大伪圆锥运动对捷联导航系统的不利影响.因此在实际应用当中,应当结合圆锥运动和伪圆锥运动对系统的影响比重,选择合适的圆锥补偿算法.     

Shock wave-induced bubble motion

There is a lack of data on transient interphase shear forces on bubbles. The present work is an experimental and analytical investigation of unsteady bubble motions induced by shock waves. Bubble trajectories were monitored in a shock tube using high-speed Schlieren photographs. Pressure histories at two locations weere used to determine the average wave speed in the bubbly mixture. An equation of motion was developed and solved for predicting the bubble trajectories and velocities. Reasonable agreement is obtained between the experimental results and the analytical predictions. It was found that for experimental range of Reynolds numbers (200 – 12,000), a constant drag coefficient $\text{c}{}_{\mathrm{D}}\text{? 2.6}$ can be utilized to estimate the drag force.     

点的复合运动中相对运动的描述

给出了点的复合运动中,动点的绝对运动方程和相对运动方程之间关系的描述方法,并将其应用于确定平面运动机构中选取不同动点和动系时的相对运动轨迹.该方法的推导过程简单易懂,易于实现,可以帮助学生在学习相关知识时对不同情况下的相对运动有清晰、直观的了解.特别是当相对运动非常复杂时,可以借助该分析过程给出相对运动轨迹曲线.     

Elementary aspects of vortex motion

Several aspects of vortex motion are considered, with a special stress on the present status of idealization, such as point vortices or vortex filament. As an introduction, elements of vortices induced by the transient flow past an obstacle are considered and their role and development are stated.

Following this introduction, a general survey of the issues in this symposium is made sketchily. As an example, the motion of point vortices in the presence of an external flow or a boundary is discussed on the basis of the Hamiltonian formalism. The cases of linear flow and semicircular boundary are taken as examples of regular and chaotic motions. Secular behaviour of a pair of vortices in the flow is remarked.     

Nonlinear wave motion in magnetoelasticity

Archive for Rational Mechanics and Analysis -     

Surface activity and bubble motion

This paper reviews recent progress in the theories of the surface boundary conditions of adsorbed solutes in liquids, and of the effects of those solutes on the steady motion of a bubble or drop in the liquid. Both singular perturbation theory and numerical solutions have useful roles in this problem, and their relationship is explored. In addition, analytical solutions are given to two problems concerning a spherical bubble rising steadily at low Reynolds number in a viscous fluid. One of these is displacement of the internal vortex centre from its position in the absence of surface activity when there is a small stagnant cap of surfactant at the rear. The results agree with experimental data in the direction of that displacement but give only about half its amount. The other problem is the velocity perturbation all round the surface caused by a very dilute solution of a weak surfactant at high Péclet number. This compares quite well with the numerical solution for a Péclet number of 60, having relative errors of order (60)^–1/2 as would be expected.     

Droplet interactions in thermocapillary motion

The dynamics of two spherical droplets, whose movement is driven by variations in interfacial tension caused by a temperature gradient, are analyzed using a method of reflections. Both droplets have the same internal fluid properties but may differ in size, and the configuration of the droplets is arbitrary relative to the direction of the undisturbed temperature gradient. The method of reflections is based on an analysis of the thermal and hydrodynamic disturbances produced by a single droplet placed in an arbitrarily varying temperature field. The results for two-droplet interactions are correct to 0(r⁻⁶) where r is the center-to-center distance between the droplets. For the specific case of bubbles oriented parallel with the undisturbed temperature gradient, my results agree very well with numerical calculations found in the literature. The results for two, identical droplets are used to find the 0(ø) effect on mean droplet velocity of a bounded suspension, where ø is the volume fraction of the droplets. In general, the interactions between droplets moving by thermocapillary effects are much weaker than in the case of sedimentation.     

Global motion of the celt

The motion of the celt attracts researchers’ attention by unusual properties. If we put the celt on a horizontal surface and twist it about its vertical axis, then, after a certain time, it stops rotating about this axis, but vibrations about the other axes may arise and then the celt begins rotating about the vertical axis in the opposite direction.Apparently, the first publications about the celt are [1, 2].The known studies of the celt motion contain some simplifying assumptions and usually perform only a local stability analysis of steady-state rotations. Of the numerous publications, we mention [3, 4], where detailed references can be found.We note that the frequently encountered assumption that the velocity of the celt point of contact with the plane is zero (a nonholonomic statement of the problem) has not been confirmed by physical considerations and must be justified separately.In the present paper, we consider the global motion of the celt for the case in which the interaction of the celt with the plane on which it moves is determined by the forces taking into account the mutually depending sliding and twisting, which makes them really physically meaningful [5]. Another example of application of dry friction model used in the present paper can be found in [6].     

动点选取法的剖析

本通过点的合成运动中动点系两种不同选法利弊的剖析,说明动点动系选取应该遵循的基本原则。     

机构运动的全程分析法

针对机构运动的“瞬时分析法”存在的问题,强调应该运用构件运动方程的联系对机构运动进行“全程分析”,并以牛头刨床机构为例对其运动的全程进行了数值计算与分析。     

Unstable crack motion is predictable

Yoffe's linear theory of dynamic brittle fracture suggests that crack motion will be unstable beyond ∼70% of the Rayleigh speed, a prediction that is not supported by experiment. We show by atomistic simulations that hyperelasticity, the elasticity of large strains, plays a governing role in the instability dynamics of brittle fracture. A simple, yet remarkable, scaling model based on an effective elastic modulus (the secant modulus at the stability limit) gives successful predictions for the onset speed of the crack instability.     

Chaotic motion and stochastic excitation

In this paper, one considers dynamic chaotic/stochastic systems and the associated Gibbs set. The behavior of these sets leads one to characterize the systems and to calculate the values of the Kolmogorov entropy. The ultimate objective is to extend an approach typical of the statistical mechanics to the analysis of systems of the mechanical engineering.     

Weakly nonlinear magnetohydrodynamic wave motion

One-dimensional magnetchydrodynamic (mhd) waves are treated including nonlinearity up to the second order in the wave amplitude; particular emphasis is on the effects of the diffusivity of the electromagnetic field on plane wave propagation. Unidirectional propagation is either governed by an equation of the Varley-Rogers type in the high frequency limit or by the Burgers equation in the low frequency limit. External resonant excitation in a finite layer leads to equations well known from resonance in various other physical systems.