Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.     

关于Smarandache可乘函数的均值研究

本文的主要目的是利用初等方法研究Smarandache可乘函数在简单数集中的均值性质,并给出一个有趣的渐近公式。     

求非线性方程近似解的逐次迭代法

本文提出了求解非线性问题的一种新方法——逐次迭代法，本方法先是给出一个初始近似解，然后将这个近似解进行校正迭代，使之接近于真实解，把一个非线性问题转化为一个线性问题来解决。     

A Review of Dynamic Fracture Studies in Functionally Graded Materials

Abstract:  This article presents a review of dynamic fracture studies on functionally graded materials. A brief literature review on the fracture mechanics of graded materials is presented first. This is followed by a discussion on the higher-order asymptotic analysis of the transient elastic field surrounding the tip of a dynamically growing crack in a functionally graded material. A comprehensive experimental study of dynamic crack growth in model functionally graded material using the optical method of reflection photoelasticity and high-speed photography is then presented. The results are analysed to establish a generalised relationship between the crack velocity and the dynamic mode-I stress intensity factor (SIF). This relationship is found to be unique and is distinctly different from that previously established for the matrix material (polyester). Finally, an innovative experimental procedure is used to demonstrate the necessity of employing a fully transient stress-field representation in the analysis of optical data for an accurate prediction of the dynamic SIF history.     

In the theory of blast waves

The behavior of the blast wave from an exploding spherical volume is investigated mathematically over the entire range of blast-wave propagation. The computational method uses analytical results for a similar problem for a point explosion with counter pressure and the theory of an asymptotically equivalent point explosion. The asymptotic solution of the gas-dynamic equations away from the explosion site is matched to the initial conditions of blast-wave formation due to the disintegration of the detonation shock upon its arrival at the boundary of the exploding volume. The spatial distribution of the blast-front pressure is found for combustible gaseous systems and solid explosives. The theoretical results obtained agree quantitatively with available experimental measurements. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 4, pp. 93–99, July–August, 2006.     

SPECTRAL DENSITY ESTIMATION FROM NONLINEARLY OBSERVED DATA

Abstract. The estimation of the spectral density function of a stationary Gaussian process at the input of an instantaneous nonlinearity is considered when the nonlinearity is known and a finite set of observations of the output process is given. A class of spectral estimates is considered and their quadratic-mean consistency is established; precise asymptotic expressions for their bias and covariance are derived and their asymptotic normality is obtained.     

保序回归的大样本性质

利用保序回归与极大似然估计之间的关系,从极大似然估计解的大样本性质出发,得到了保序回归解的两个大样本性质。     

How to Control Robots Interacting with Dynamic Environment

The goal of this paper is to shed light on the control problem of constrained robot motion from the aspect of the dynamical nature of the environment with which the robot is in contact. Therefore, the criticism of traditional hybrid control which allows position/force feedback loops to split into independent control with respect to position and force, is not the main point we want to make. Reference to the papers written by the founders of hybrid control and their numerous followers served only to better understand the reason and motivation for suggesting a different approach to control of robots interacting with environment.The paper has a predominantly review character, based on recently published work. It also contains some new, unpublished results in the framework of the unified approach to the position/force control of robots, proposed by the present author and his co-workers. By pointing to the possibility of introducing an environment dynamics in the contact tasks of the machining type, the author emphasizes that the proposed dynamically interactive control can be applied to a completely different class of tasks, in which a contact is made between the system (constructions or structure) and very specific kinds of dynamic environments.     

Ultrasonic nondestructive evaluation of fibre-reinforced composite materials — a review

A framework is presented for examining the effectiveness of limiting and modelling arguments used in the analysis of fluid flows. It consists of examining the consequences of the arguments on the flow problem as a whole and breaking down the limiting/modelling process into a sequence of steps and associated sequence of flow problems, termed here as ‘lidels’. The notion of validity of lidels is given. Several examples are given to explain the present approach. Invited general lecture at 3rd ACFM, Tokyo, September 1986     

转子系统热膨胀状态下固有横振频率

把转子的惯性力看成作用在轴上的外力,采用新的非线性渐近法研究热膨胀对转子系统固有横振频率的影响.