具有完整约束的变质量系统的机械能守恒律

研究具有双面理想完整约束的变质量力学系统的机械能守恒律.首先,利用系统的运动微分方程,获得能量变化方程,并给出机械能守恒律存在的充分必要条件.然后,提出具有守恒律的27种情形.最后,举例说明.     

经典非完整Appell Hamel约束的性质

研究了非完整约束Appell-Hamel例.证明了经典Appell-Hamel例对于非完整系统的Hamilton作用量是稳定值.研究了该约束对于非完整力学Rosen-Edelstein模型的解,证明了对于三个非完整力学模型Ap-pell-Hamel例具有相同解.利用非完整力学系统可归结为有条件的完整系统的理论,得出了经典Appell-Hamel例具有第二类Lagrange方程的形式.     

Nielsen方程的三重组合梯度表示及其稳定性分析

研究Nielsen方程的三重组合梯度表示以及方程零解稳定性.首先给出4类三重组合梯度系统及其性质.其次,给出完整系统和非完整系统的Nielsen方程转化成三重组合梯度系统的条件;将完整和非完整两类Nielsen方程分别化为三重组合梯度系统并研究方程的零解稳定性.最后,举例验证结果的应用.     

力学与控制科学

基于对力学与控制科学的相似性的分析,阐述了4个有意义的力学系统控制问题:① 具非完整约束的非线性动力学系统的控制;②具非单一平衡位置的力学系统及其总体性质;③ 多体动力学与控制;④具分布参数的力学系统.最后给出了一个具启示性的看法.     

α方法在非完整力学系统数值积分中的应用

将源于直接积分方法的广义-α法和d—RATTLE法应用到非完整力学系统动力学方程数值积分中,直接求解指标-2的微分一代数方程（DAEs）,这两种方法的质量矩阵可以是常量,也可以与广义坐标相关．最后,文中通过一个非完整力学系统：Snakeboard模型,对这两种方法进行了验证,并且与DASSL算法包的结果进行了比较．     

基于球摆模型的离散变分积分子算法研究

在动力学系统长时间的仿真计算中,力学系统固有的结构将影响到计算精度及稳定性.离散变分积分子能够保持力学系统的能量,动量及辛结构的守恒.结合离散变分原理,通过对系统的拉格朗日函数进行离散化以及求变分和积分的过程,可以得到力学系统的离散变分积分子算法.该算法是一种递归算法,给定初始条件便可得到系统的动力学参数的时间历程.使用该原理可以构造具有完整约束的拉格朗日系统的辛-动量积分子方法.与连续算法相比,离散变分积分子算法能够直接在离散拉格朗日函数的基础上得到姿态与角速度的递推公式,而不需要复杂的迭代计算.本文研究是基于第一类拉格朗日函数的离散变分积分子算法.球摆模型是一个具有完整约束的拉格朗日系统.仿真结果表明,系统的能量值在长时间的仿真中得到保持,且计算的精度与步长的数量级呈现二次方的关系,系统角速度和姿态的仿真结果都符合球摆的运动规律.     

变质量力学系统的Herglotz型Lagrange方程与Noether对称性和守恒量

Herglotz变分原理提供了非保守耗散问题的变分描述，同时变质量力学在自然界和工程领域有大量的应用，因此将Herglotz变分原理应用于变质量力学系统的Lagrange方程与守恒律研究，为研究变质量力学提供了一个新的途径.文中建立了变质量力学系统的Herglotz型广义变分原理，导出了变质量系统的Herglotz型Lagrange方程.定义了变质量力学系统的Herglotz型Noether对称性，建立并证明了Herglotz型Noether定理及其逆定理.文末给出两个变质量非保守系统的具体例子以说明结果的应用.     

事件空间中非完整力学系统的Herglotz-d′Alembert原理与守恒律

研究事件空间中非完整力学系统的Herglotz型守恒律.给出事件空间中Herglotz型广义变分原理,引入非完整约束并采用交换关系的H9lder定义,导出事件空间中非完整力学系统的新型微分变分原理—Herglotz-d′Alembert原理.引进事件空间中的空间生成元和参数生成元,建立Herglotz-d′Alembert原理不变性条件的变换.基于该原理构建了事件空间中非完整非保守力学系统的Herglotz型守恒定理及其逆定理.作为特例,给出了位形空间的Herglotz型守恒量和事件空间中完整力学系统的Herglotz型守恒量.文末还给出了一个算例.     

关于分析力学的基础与展望

本文从分析约束力学系统的“欠定”问题开始,介绍分析力学的基本变分原理和三类运动微分方程,并分析了分析力学具有普适性之缘由.对非完整约束力学系统,着重分析其动力学建模问题、几何结构和重点发展方向,同时又简要介绍了Birkhoff系统所具有的一般辛结构特征和研究意义,以及需要重点解决的问题.文中对力学系统的Noether对称性和运动微分方程的对称性作了较为详细的论述,并列举了相应实例说明两种对称性与守恒量之间的关系.在几何力学部分,重点介绍了分析力学的辛几何结构和对称性约化理论,包括辛流形的Darboux Moser Weinstein局部正则结构、整体拓扑结构及其对量子力学的影响、Lie群与Lie代数的伴随表示和余伴随表示、动量映射、Cartan辛约化、Marsden Weinstein约化等.文中最后论述了完整与非完整力学系统可积性问题的研究方法和成果,指出了非完整力学系统现有可积性方法的局限性.     

有多余坐标的可控完整力学系统的自由运动与初始运动

对于完整力学系统,若选取的参数不是完全独立的,则称为有多余坐标的完整系统.本文研究有多余坐标的可控力学系统的自由运动与初始运动.首先,需由d′Alembert Lagrange原理并利用Lagrange乘子法建立有多余坐标完整系统的运动微分方程;其次,由约束系统自由运动的定义,令所有乘子为零,得到系统实现自由运动的条件.第三,如果给定运动的初始条件和控制参数,就可以研究系统的初始运动.文末,举例并说明方法和结果的应用.     

Control of wheel system with regard for state measurement errors

Consideration was given to the nonholonomic mechanical systems with rolling or the wheel systems. Analysis was confined to the kinematic models. Dynamics of the controlling actuator was taken into account. Consideration was given to the control of a system moving along the given trajectory. The constructed law of control stabilizes this motion as a whole in the main variables. The basic result is concerned with substantiating stability with regard for the errors of measuring the system state.     

Study of the internal dynamics of an autonomous mobile robot

The requirement of ideal rolling without sideways slipping for wheels imposes nonholonomic (non-integrable) constraints on the motion of the wheels and consequently on the motion of wheeled mobile robots. From the control point of view, the dynamics of nonholonomic systems can be divided in two parts: external and internal dynamics. The dimension of the external dynamics of nonholonomic systems depends on the number of inputs to the system and the dimension of the internal dynamics depends on the number of independent nonholonomic constraints. For different motion control problems of nonholonomic systems, a smooth (model based) state feedback control law only deals with the system external dynamics; therefore, the system internal dynamics must be examined separately and its stability has to be analyzed and proved.In this paper, the internal dynamics of a three-wheel mobile robot with front wheel steering and driving is investigated. In particular, its internal dynamics stability is analyzed for two different situations, when the mobile robot is moving and when it is stationary.     

A control of a wheeled system with account of side slip

The control problem for wheeled systems similar to a mobile robot, a vehicle, a wheeled tractor, and so on, is studied. These systems are referred to the class of nonholonomic mechanical systems, the analysis is limited to kinematic models, and the dynamics of control drives is taken into account. A control that stabilizes the motion of a wheeled system along a given trajectory (planar smooth curve) is constructed. The stabilizability is substantiated in large with respect to basic variables of the system. The central result is connected with the proof of motion stability when the side slip of the system wheels is taken into account.     

Robust motion tracking control of partially nonholonomic mechanical systems

This paper proposes a stable motion tracking control law for mechanical systems subject to both nonholonomic and holonomic constraints. The control law is developed at the dynamic level and can deal with model uncertainties. The proposed control law ensures the desired trajectory tracking of the configuration state of the closed-loop system. A global asymptotic stability result is obtained in the Lyapunov sense. A detailed example is presented to illustrate the proposed method.     

Efficient formulation of the Gibbs–Appell equations for constrained multibody systems

Multibody System Dynamics - In this study, we present explicit equations of motion for general mechanical systems exposed to holonomic and nonholonomic constraints based on the Gibbs-Appell...     

Steering for a class of dynamic nonholonomic systems

We derive control algorithms for a class of dynamic nonholonomic steering problems, characterized as mechanical systems with nonholonomic constraints and symmetries. We use a simplified geometric framework in developing two types of control algorithms for such systems. The first targets local configuration controllability, using a perturbation approach to establish results similar to steering using sinusoids. The second method builds on this approach by utilizing kinematic steering algorithms for mobile robots in generating more nonlocal motion plans for this class of systems     

An alternative algebra for deriving equations of motion of flexible manipulators

An alternative means for deriving equations of motion of complex systems is demonstrated. Since the method is energy based, it is useful for elastic systems. Because the method can handle vectors expressed relative to rotating coordinate systems, it does not require the introduction of coordinate transformations and thereby produces equations in a simple form. The article shows that Kane's method for rigid body systems is a special case of this alternative method. Two example problems show how the algebra can be applied to rigid and flexible nonholonomic systems.     

A Systematic Approach for Designing Analytical Dynamics and Servo Control of Constrained Mechanical Systems

A systematic approach for designing analytical dynamics and servo control of constrained mechanical systems is proposed. Fundamental equation of constrained mechanical systems is first obtained according to Udwadia-Kalaba approach which is applicable to holonomic and nonholonomic constrained systems no matter whether they satisfy the D'Alember's principle. The performance specifications are modeled as servo constraints. Constraint-following servo control is used to realize the servo constraints. For this inverse dynamics control problem, the determination of control inputs is based on the Moore-Penrose generalized inverse to complete the specified motion. Secondorder constraints are used in the dynamics and servo control. Constraint violation suppression methods can be adopted to eliminate constraint drift in the numerical simulation. Furthermore, this proposed approach is applicable to not only fully actuated but also underactuated and redundantly actuated mechanical systems. Two-mass spring system and coordinated robot system are presented as examples for illustration.      

Motion planning in velocity affine mechanical systems

We address the motion planning problem in specific mechanical systems whose linear and angular velocities depend affinely on control. The configuration space of these systems encompasses the rotation group, and the motion planning involves the system orientation. Derivation of the motion planning algorithm for velocity affine systems has been inspired by the continuation method. Performance of this algorithm is illustrated with examples of the kinematics of a serial nonholonomic manipulator, the plate-ball kinematics and the attitude control of a rigid body.