平底顶杆凸轮机构的MATLAB动画编程

 给出了一个用MATLAB语言编制的动画文件，用于演示平底顶杆凸轮机构运动过程以及 动点的相对运动轨迹. 对该程序稍加修改，即可演示理论力学中其它机构运动的过程 及相关轨迹.     

关于动点动系的选择原则

如何正确地选择动系、动点的问题,一般地说应遵循如下的三条原则。(1) 动点在动系中一定要有相对运动。(2) 动点的相对运动轨迹要易于确定。所以要求动点在运动过程中始终是两个运动部件的接触点。(3) 动系的牵连运动要易于分析确定。如平动、定轴转动、平面运动等等。动点动系选择得正确与否是求解平面运动问题的...     

相对运动分析中的一个难点

在用复合运动概念分析点的运动时,如何分析点的相对运动,特别是相对运动轨迹,是相对运动分析中的一个难点。本文以平板凸轮机构为例,先介绍错误的分析,然后分析错误的微结所在并具体地阐述相对运动的分析方法。例:偏心轮半径为r,偏心距oc=e以角速度 ...     

动轴理论及其应用——理论力学札记之十

动轴理论是指用相对动轴系的运动来列写质点或刚体的动力学方程的理论.动轴系可以固连于刚体上,也可以不固连于刚体上.动轴理论给出的方程,有时是方便的.     

动点动系的选择方法与相对运动轨迹的几何性质

应用点的复合运动理论对机构等进行运动分析时,选择动点与动系应考虑以下两点: (1) 使要建立的运动学关系式中,既包含已知量,又包含待求量(或中间量); (2) 使相对运动轨迹简单或直观。两点相互补充,后者更为重要。否则,即使勉强定出相对速度v_r的方向,求得速度未知量,但却因相对轨迹曲率半径ρ_r未知,而无法使相对加速度中两个 ...     

基于鲁棒滤波的无人机着陆相对导航方法

针对无人机在移动平台上进行起降时的相对导航问题,提出了一种基于鲁棒高阶容积滤波的惯导/视觉相对导航方法。建立了相对导航系统模型,基于无人机与移动平台之间的相对运动给出了系统的相对惯导方程,并针对系统中传感器的量测特性给出了导航敏感器的测量方程。针对相对导航系统非线性较强且量测噪声不符合高斯分布等问题,在高阶容积滤波的基础上,结合Huber-based量测更新方程,设计了鲁棒高阶容积滤波相对导航滤波器,该方法具有较高的估计精度,且对混合高斯噪声有鲁棒性。相对姿态采用四元数表示,为保证四元数的归一化,在设计相对导航滤波器时采用修正的罗德里格斯参数表示姿态误差。仿真结果表明,该方法可以准确地给出无人机与移动平台之间的相对位置、速度和姿态信息,且估计精度高于扩展卡尔曼滤波、Huber-Based滤波以及高阶容积卡尔曼滤波。     

平面运动刚体两类瞬心轨迹之间关系的探讨

首先阐述了刚体运动的列阵-矩阵描述方法,然后在阐明刚体瞬心及两类瞬心轨迹等概念的基础上,经过简洁的数学推演,给出了平面运动刚体的动瞬心轨迹与定瞬心轨迹在固定坐标系中投影的运动方程.通过分析二者的运动方程,证明了结论:平面运动刚体任一时刻的动瞬心轨迹在定瞬心轨迹上作纯滚动,接触点即为刚体在该时刻的瞬心固连点.然后通过一个具体算例展示了瞬心轨迹运动方程的求解方法,并讨论了运动方程的物理意义.最后对一般运动刚体的情形进行了简要讨论.     

径向运动方程在绝对、相对坐标系下的相互转换

针对叶轮机械中绝对坐标系下径向运动方程与相对坐标系下径向运动方程相互转换的问题进行了讨论,给出了相应的推导过程,澄清了一些关于该问题的解释.     

动力学普遍定理对非完整动力学的应用——分析力学札记之二十九

研究非完整动力学问题,可用理论力学方法或分析力学方法.理论力学方法用动力学普遍定理建立运动方程:分析力学方法用非完整动力学的各类方程来列写系统的运动方程.动力学普遍定理,特别是动量矩定理可以用于定点、质心或动点.有时对动点的动量矩定理比对定点的或质心的要简单得多.     

精密离心机动平衡的力学性能分析

本文建立了惯导器件测试用精密离心机动平衡的动力学方程,给出了不平衡与电容测微仪输出振动位移之间的关系,得到了不平衡作用下精密离心机主轴几何轴线上各点运动方程及运动轨迹.     

Global motion of the celt

The motion of the celt attracts researchers’ attention by unusual properties. If we put the celt on a horizontal surface and twist it about its vertical axis, then, after a certain time, it stops rotating about this axis, but vibrations about the other axes may arise and then the celt begins rotating about the vertical axis in the opposite direction.Apparently, the first publications about the celt are [1, 2].The known studies of the celt motion contain some simplifying assumptions and usually perform only a local stability analysis of steady-state rotations. Of the numerous publications, we mention [3, 4], where detailed references can be found.We note that the frequently encountered assumption that the velocity of the celt point of contact with the plane is zero (a nonholonomic statement of the problem) has not been confirmed by physical considerations and must be justified separately.In the present paper, we consider the global motion of the celt for the case in which the interaction of the celt with the plane on which it moves is determined by the forces taking into account the mutually depending sliding and twisting, which makes them really physically meaningful [5]. Another example of application of dry friction model used in the present paper can be found in [6].     

捷联惯导系统中的圆锥和伪圆锥运动研究

分别对圆锥运动和伪圆锥运动的产生原因、表达形式,以及对捷联惯导系统的影响进行了分析.由于圆锥运动和伪圆锥运动并不相同,因此圆锥运动补偿算法将对两者产生不同的效果.数字仿真表明,圆锥补偿算法可以大大降低经典圆锥运动对捷联导航系统的不利影响,但同时却会增大伪圆锥运动对捷联导航系统的不利影响.因此在实际应用当中,应当结合圆锥运动和伪圆锥运动对系统的影响比重,选择合适的圆锥补偿算法.     

刍议点的牵连运动的定义

简要介绍,讨论了各种力学献中关于点的牵连运动的4种定义,通过综合分析比较,认为第4种定义较为恰当。     

On the instability of steady motion

This paper deals with the instability of steady motions of conservative mechanical systems with cyclic coordinates. The following are applied: Kozlov’s generalization of the first Lyapunov’s method, as well as Rout’s method of ignoration of cyclic coordinates. Having obtained through analysis the Maclaurin’s series for the coefficients of the metric tensor, a theorem on instability is formulated which, together with the theorem formulated in Furta (J. Appl. Math. Mech. 50(6):938–944, 1986), contributes to solving the problem of inversion of the Lagrange-Dirichlet theorem for steady motions. The cases in which truncated equations involve the gyroscopic forces are solved, too. The algebraic equations resulting from Kozlov’s generalizations of the first Lyapunov’s method are formulated in a form including one variable less than was the case in existing literature.     

Modeling the motion of connected bodies

Spatial motion of mechanical systems consisting of jointed rigid bodies is considered. The methods previously developed to solve the dynamic equations of “carrier + loads” systems analytically for the accelerations of individual bodies are used to obtain the equations of motion of systems with complicated branched structure. The following practically important cases are analyzed: (i) a central carrier with peripheral loaded carriers and (ii) a chain and a ring consisting of loaded carriers. Numerical results are given for the stress-strain state of an elastic spacecraft represented as a chain of rigid bodies connected by elastic joints.     

Calculation of the motion of two-component media

The one-dimensional motion of a viscous incompressible liquid in which particles are suspended is described by the mathematical model used in [1], Two examples are discussed: the precipitation of particles from the suspension, and a boiling layer. The results are presented in the form of graphs.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 102–108, November–December, 1973.     

Analysis of the motion of a gyro-theodolite

With the method of analytical mechanics, this paper studies the motions of a gyrotheodolite under the action of (1) the torque of gravity only, (2) the torque applied by the band suspension, (3) the torque of the band suspension with air damping considered, the equations of motion are then established and their solutions are found. Furthermore, analysis of the law of motion and the behaviour of gyro-theodolite during the orientation is made.     

Stabilization of the motion of linear systems

Kiev Machine Works. Translated from Prikladnaya Mekhanika, Vol. 27, No. 5, pp. 107–110, May, 1991.