Reflections on the Gauss Principle of Least Constraint

The Gauss principle of least constraint is derived from a new point of view. Then, an extended principle of least constraint is derived to cover the case of nonideal constraints. Finally, a version of the principle for general underdetermined systems is adumbrated. Throughout, the notion of generalized inverses of matices plays a prominent role.     

New Conserved Quantities of Noether-Mei Symmetry for Nonholonomic Mechanical System

Two new types of conserved quantities deduced by Noether-Mei symmetry of nonholonomic mechanical system are studied. The definition and criterion of Noether-Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether-Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether-Mei symmetry of mechanical system can be obtained.     

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

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