A method for relaxing parameter constraints in rigid body dynamics

As attractive alternatives to a set of three Euler angles, the rotation of a rigidly deforming body is often represented using four or more parameters. The accompanying parameter constraints introduce generalized constraint forces in the equations of motion which can often negate the benefits of a particular parameterization. In this paper, we discuss situations where the parameter constraints are not imposed. Thus, although the body no longer deforms rigidly, it does deform homogeneously. This allows the theory of a Cosserat point (or, equivalently, the theory of a pseudo-rigid body) to be used to establish equations governing its motion. Earlier work on this topic by O’Reilly and Varadi considered the four Euler parameters and the single Euler parameter constraint. Here, we consider Poincaré's six parameter representation of a rotation tensor, and, complementing earlier work, discuss numerical implementation and representative simulations. One of the contributions of this paper is the development of a viscoelastic Cosserat point, whose equations of motion are free from parameter constraints and singularities, that can be used to approximate the motion of a rigid body.     

Effect of Boundary-Layer Thickness on the Structure of a Near-Wall Flow with a Two-Dimensional Obstacle

Results of physical and numerical experiments on investigating the effect of the depth of immersion of a two-dimensional obstacle with a square cross section into a developed turbulent boundary layer on the length of the separated flow region are presented. The numerical simulation is based on solving averaged Navier–Stokes equations with the use of the k– model of turbulence. The near-wall flow is visualized in the experiments, and the fields of mean and fluctuating velocities are measured. Flow regions where the results of numerical simulation agree with experimental data are determined. It is shown that the length of the recirculation flow region in the near wake increases with decreasing depth of immersion of the two-dimensional obstacle into the turbulent boundary layer.     

New control laws for stabilization of a rigid body motion using rotors system

This paper presents a new class of globally asymptotic stabilizing control laws for dynamics and kinematics attitude motion of a rotating rigid body. The rigid body motion is controlled with the help of a rotor system with internal friction. The Lyapunov technique is used to prove the global asymptotic properties of the stabilizing control laws. The obtained control laws are given as functions of the angular velocity, Cayley–Rodrigues and Modified-Rodrigues parameters. It is shown that linearity and nonlinearity of the control laws depend not only upon the Lyapunov function structure but also the rotors friction. Moreover, some of the results are compared with these obtained in the literature by other methods. Numerical simulation is introduced.     

Rotating Variable-thickness Orthotropic Cylinder Containing a Solid Core of Uniform-thickness

This paper presents accurate elastic solutions for the rotating variable-thickness and/or uniform-thickness orthotropic circular cylinders. The present circular cylinder may contain a uniform-thickness solid core of rigid or homogeneously isotropic material. Different cases of rotating cylinders of various cores are investigated. These cylinders include completely isotropic solid cylinder, uniform-thickness orthotropic cylinder containing an isotropic core, variable-thickness orthotropic cylinder containing an isotropic core, uniform-thickness orthotropic cylinder containing a rigid core, and variable-thickness orthotropic cylinder containing a rigid core. For all cases studied, exact elastic solutions are obtained and numerical results are presented. The results include the radial, hoop, and axial stresses and radial displacement of the five cylinder configurations. The distributions of displacement and stresses through the radial direction of the rotating cylinder are obtained and comparisons between different cases are made at the same angular velocity.     

The effect of velocity on rigid wheel performance

A simulation model to predict the effect of velocity on rigid-wheel performance for off-road terrain was examined. The soil–wheel simulation model is based on determining the forces acting on a wheel in steady state conditions. The stress distribution at the interface was analyzed from the instantaneous equilibrium between wheel and soil elements. The soil was presented by its reaction to penetration and shear. The simulation model describes the effect of wheel velocity on the soil–wheel interaction performances such as: wheel sinkage, wheel slip, net tractive ratio, gross traction ratio, tractive efficiency and motion resistance ratio. Simulation results from several soil-wheel configurations corroborate that the effect of velocity should be considered. It was found that wheel performance such as net tractive ratio and tractive efficiency, increases with increasing velocity. Both, relative wheel sinkage and relative free rolling wheel force ratio, decrease as velocity increases. The suggested model improves the performance prediction of off-road operating vehicles and can be used for applications such as controlling and improving off-road vehicle performance.     

A dynamic terramechanic model for small lightweight vehicles with rigid wheels and grousers operating in sandy soil

This paper presents a validated dynamic terramechanic model for rigid wheels with grousers that may be used for planetary and terrestrial mobile robots operating in loose sandy soil. The proposed model is based on established analytical terramechanic theories and incorporates two new dimensionless empirical coefficients. The additional terms in the model are based on existing soil mechanic theories that vary as a function of soil properties, slip conditions, and vehicle loading. The proposed model was able to capture and predict the dynamic oscillations observed in experimental data from a single-wheel testbed for the sinkage, drawbar pull and normal load. For the operating conditions tested in this research the simulation results using the proposed model show an improvement over traditional terramechanic models for capturing the dynamic effects of grousers.     

Optimal investment with transaction costs based on exponential utility function: a parabolic double obstacle problem

This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method.     

柔性障碍物对甲烷空气爆炸波激励作用的实验研究

为研究柔性障碍物对甲烷空气爆炸波的激励效应,采用双向拉伸聚丙烯（biaxially oriented polypropylene, BOPP）薄膜作为柔性障碍物将管道内甲烷空气预混气体与空气隔开,对比障碍物前后火焰、激波变化,分析膜状柔性障碍物激励效应的机理。实验结果表明:这种具有一定承压能力的柔性障碍物对甲烷爆炸波产生的激励效应不可忽视,在膜片破裂前产生多次激波反射过程,可诱导湍流火焰形成,促使膜前爆炸压力提高,膜片破裂后,火焰在伴流作用下传播速度突增,并加速逐渐逼近前驱冲击波,致使膜后爆炸压力大幅提高;激励效应可使膜片前后最大爆炸压力相差5倍,火焰速度相差7倍;另外在膜片位置2.5 m后增设一道膜片,可增强这种激励效应,而增加膜片的实质是使激波火焰相互作用的次数增加。     

Zeros of the Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering

Some novel interlacing properties of the zeros for the Besseland spherical Bessel functions are first presented and thenapplied to prove an interesting uniqueness result in inverseacoustic obstacle scattering. It is shown that in the resonanceregion, the shape of a sound-soft/sound-hard ball in R³ or asound-soft/sound-hard disc in R² is uniquely determined by asingle far-field datum measured at some fixed spot correspondingto a single incident plane wave.     

电磁散射问题手性障碍边界重构的线性探测法的理论分析

In this paper,we consider the inverse scattering by chiral obstacle inelectromagnetic fields,and prove that the linear sampling method is also effective todetermine the support of a chiral obstacle from the noisy far field data.