De Bruijn序列的k次齐次复杂度

De Bruijn序列是一类最重要的非线性移位寄存器序列。本文定义并研究了n级De Bruijn序列的k次齐次复杂度C_k(s),给出了C_k(s)的一个上界。k=1及k=2时,C_k(s)分别为人们所熟知的线性复杂度及二次齐次复杂度。

欠驱动航天器姿态稳定性的齐次控制方法

应用齐次控制方法研究欠驱动航天器姿态稳定性问题。采用(w,z)参数描述航天器姿态的运动,在无扰力矩的假设下,给出欠驱动航天器的姿态动力学方程。通过分析系统模型的特点,确定系统的向量场f为齐次的,利用齐次系统理论和齐次反馈设计欠驱动航天器姿态角速度ωx和ωy的控制律,使系统姿态参数和角速度w1、w2、ωz趋于渐近稳定。数值仿真实验验证了控制律的有效性。

Two algorithms of working acceleration generated by a precision centrifuge with two rotating axes

The displacement of the origin of the accelerometer coordinate system relative to the origin of the base coordinate system is calculated by homogeneous transformation. The second order derivative of this displacement is the acceleration of the origin to the accelerometer coordinate system. By means of the attitude relationship between the base coordinate system and the accelerometer coordinate system, the acceleration components on the three coordinate axes is obtained. Utilizing the Coriolis rotation coordinate theorem, the three components are also calculated. The homogeneous transtbrmation method and vector differential method lead to identical results.

Direct calculation of acceleration field through homogeneous transformation for two-axis centrifuge

A precision centrifuge is an inertial navigation test equipment used for calibrating the characteristics of accelerometers with high overloading, and a two axis centrifuge can be used to generate either constant acceleration or harmonic acceleration. The moving trajectory equation about the origin of the accelerometer coordinate system in a two axis centrifuge was directly deduced through homogeneous transformation. The acceleration vector of the origin in accelerometer coordinate system was achieved by making the second derivative of this trajectory equation. The acceleration components were acquired by decomposing this acceleration vector along the three axes of the accelerometer coordinate system. The correctness of the homogeneous transformation was verified through vector analysis.

Automatic DEXP method derived from Euler’s Homogeneity equation

The depth from extreme points(DEXP)method can be used for estimating source depths and providing a rough image as a starting model for inversion.However,the application of the DEXP method is limited by the lack of prior information regarding the structural index.Herein,we describe an automatic DEXP method derived from Euler’s Homogeneity equation,and we call it the Euler–DEXP method.We prove that its scaling field is independent of structural indices,and the scaling exponent is a constant for any potential field or its derivative.Therefore,we can simultaneously estimate source depths with diff erent geometries in one DEXP image.The implementation of the Euler–DEXP method is fully automatic.The structural index can be subsequently determined by utilizing the estimated depth.This method has been tested using synthetic cases with single and multiple sources.All estimated solutions are in accordance with theoretical source parameters.We demonstrate the practicability of the Euler–DEXP method with the gravity field data of the Hastings Salt Dome.The results ultimately represent a better understanding of the geometry and depth of the salt dome.

Exact Solutions for the Generalized KdV Equation： Modified Homogeneous Balance Method

In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several kinds of exact（new） solutions of the generalized KdV equation are obtained.

Dynamic Analysis of aSelected Spatial One-DOF Linkage Mechanism with Friction in Joints

The dynamic analysis of a one-DOF RSRRR spatial linkage mechanism, including four rotational joints R and one spherical joint S, is presented in the paper. It is assumed that friction occurs in the rotational joints, whereas a spherical joint can be treated as an ideal one. The mechanism in the form of a closed-loop kinematic chain was divided by cut joint technique into two open-loop kinematic chains in place of the spherical joint. Joint coordinates and homogeneous transformation matrices were used to describe the geometry of the system. Equations of the chains＇ motion were derived using formalism of Lagrange equations. Cut joint constraints and reaction forces, acting in the cutting place---i.e, in the spherical joint, have been introduced to complete the equations of motion. As a consequence, a set of differential-algebraic equations has been obtained. In order to solve these equations, a procedure based on differentiation twice of the formulated constraint equations with respect to time has been applied. In order to determine values of friction torques in the rotational joints in each integrating step of the equations of motion, joint forces and torques were calculated using the recursive Newton-Euler algorithm taken from robotics. For the requirements of the method, a model of a rotational joint has been developed. Some examples of results of the numerical calculations made have been presented in the conclusions of the paper.

Inverse analysis of thermal conductivities in transient non-homogeneous and non-linear heat conductions using BEM based on complex variable differentiation method

This paper presents a new inverse analysis approach to sensitivity analysis and material property identification in transient non-homogeneous and non-linear heat conduction Boundary Element Method (BEM) analysis based on Complex Variable Differentiation Method (CVDM). In this approach, the material properties are taken as the optimization variables, and the sensitivity coefficients are computed by CVDM. The advantages of using CVDM are that the computation of partial derivatives of an implicit function is reduced to function calculation in a complex domain, and the parameter sensitivity coefficients can be determined in a more accurate way than the traditional Finite Difference Method (FDM). Based on BEM and CVDM in evaluation of the sensitivity matrix of heat flux, the parameter such as thermal conductivity can be accurately identified. Six numerical examples are given to demonstrate the potential of the proposed approach. The results indicate that the presented method is efficient for identifying the thermal conductivity with single or multiple parameters.