Closed-Loop Control of the Motion of a Disk–Rod System

This work deals with the guidance and control of a system which is composed of a rolling disk and a controlled slender rod that is pivoted, through its center of mass, about the disk center. There are given N points P _i, i=1, ..., N, in the horizontal plane, a set of angles _2i , i=1, ..., N, a finite-time interval [0, t _f], and a sequence of times ₁=0<₂<...< _N =t _f. Using the concept of path controllability, a closed-loop control law is derived to steer the system in such a manner that the disk center and the rod angle of rotation ₂ will pass through (P _i, _2i ) at the times _i , i=1,...,N, respectively. This system serves as a model for the motion of a simple mobile robot.     

EFFECTS OF NONHOLONOMIC CONSTRAINT ON LIE SYMMETRIES AND CONSERVED QUANTITIES OF LAGRANGIAN SYSTEMS

After a Lagrangian system is constrained by nonholonomic constraints, the determining equations, the structure equation and the form of conserved quantities corresponding to the Lie symmetries will change. Some symmetries vanish and under certain conditions some Lie symmetries still remain.     

变质量非线性非完整系统的Gibbs-Appell方程

本文首先将Gibbs-Appell方程推广到最一般的变质量非完整系统.得到变质量非线性非完整系统在广义坐标、准坐标下的Gibbs-Appell方程和积分变分原理,最后给出一个例子.     

高阶非完整系统运动方程的一类积分

本文给出高阶非完整系统运动方程的一类积分及其存在条件,包括1阶积分(广义能量积分),2阶积分和p(p>2)阶积分,所有这些积分都可按系统的Lagrange函数来构造.举例说明本文方法的应用.     

FIRST INTEGRALS AND INTEGRAL INVARIANTS FOR VARIABLE MASS NONHOLONOMIC SYSTEM IN NONINERTIAL REFERENCE FRAMES

ＦＩＲＳＴＩＮＴＥＧＲＡＬＳＡＮＤＩＮＴＥＧＲＡＬＩＮＶＡＲＩＡＮＴＳＦＯＲＶＡＲＩＡＢＬＥＭＡＳＳＮＯＮＨＯＬＯＮＯＭＩＣＳＹＳＴＥＭＩＮＮＯＮＩＮＥＲＴＩＡＬＲＥＦＥＲＥＮＣＥＦＲＡＭＥＳＬｕｏＳｈａｏ－ｋａｉ（罗绍凯）（Ｓｈａｎｇｑｉｕ,Ｎｏｒ...     

Elastoplastic analysis of cylindrically orthotropic composite lamina with a circular hole under uniform pressure

This paper presents the standard parametric representation of the Tsai-Hill yieldcriterion in a state of plane stress and the equations governing the stress distribution in acylindrically orthotropic composite lamina with a circular hole under uniform pressure forthe three cases: (a) elastic state.(b) limit state and (c) elastoplastic state. The formulasfor the yield pressure and the limit pressure have been obtained.     

Mechanical conditions for fracture of anisotropic bodies and their geometry in stress space

The conditions for fracture of anisotropic bodies and theirgeometry in stress space are proposed in this paper.The an-alytical formulae expressing the fracture conditions are es-tablished from the viewpoint of energy theory for crack pro-pagation.In stress space the limiting surface corresponding to thefracture conditions derived for anisotropic solids is quadra-tic.It is an ellipsoid in case the mean stress is greaterthan zero and it is hyperboloid in case the mean stress is smal-ler than zero.The conclusions formed by the author in the present paperhave certain generality.Some results obtained by predeces-sors appear to be special cases with respect to the presenttheory.     

切塔耶夫型非完整系统的广义梯度表示

非定常非完整力学系统的稳定性研究是重要而又困难的问题,直接从微分方程出发来构造李雅普诺夫函数往往很难实现.本文给出了一种间接方法.提出了10类广义梯度系统的定义,并分别给出了10类广义梯度系统的微分方程.进一步研究一般切塔耶夫型非完整系统的广义梯度表示,给出该系统分别成为这10类广义梯度系统的条件,从而将切塔耶夫型非完整系统化成各类广义梯度系统.最后利用广义梯度系统的性质来研究切塔耶夫型非完整系统零解的稳定性.这种方法在直接构造李雅普诺夫函数发生困难时,显得更为有效.举例说明结果的应用.     

Determining the constraint reactions of awheeled robotic vehicle with one steerable wheel

The reactions of the nonholonomic constraints of a wheeled robotic vehicle with one steerable wheel are determined. Simplified (asymptotic) relations are derived in addition to the exact ones. They are used to estimate the reactions. The efficiency of the approximate formulas is demonstrated by an example Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 123–131, November 2008.     

Two New Types of Conserved Quantities Deduced from Noether Symmetry for Nonholonomic Mechanical System

For a nonholonomic mechanical system, the generalized Mei conserved quantity and the new generalized Hojman conserved quantity deduced from Noether symmetry of the system are studied. The criterion equation of the Noether symmetry for the system is got. The conditions under which the Noether symmetry can lead to the two new conserved quantities are presented and the forms of the conserved quantities are obtained. Finally, an example is given to illustrate the application of the results.