The stability of a top rotating on a rough horizontal plane

In the present paper the stability of permanent rotation of a symmetric top rotating on a slightly rough horizontal plane about the erect polar or transverse axis is discussed via the perturbation method. As a perturbation factor, the frictional force is an arbitrary nonlinear function of the sliding velocity. The same stability criterion as that in the Contensou-Magnus linear theory is obtained, but the hypothesis of the linearity for friction can be omitted. It shows that the direction of the sliding velocity at the contact point is an important factor, which influences the stability of the top. And then an explicit physical explanation is given.     

The development of the dynamics of rigid body with state variables

The dynamics of a rigid body can be investigated by using state variables instead of Euler's equations. Since the differential equations have a canonical form of the first order, the method mentioned has distinct advantages not only for qualitative analysis but also for numerical calculation. In the present paper the development of this method in China is summarized.     

三浮陀螺有源磁悬浮系统力学模型分析

有源磁悬浮系统在高过载条件下的工作状态,是影响三浮陀螺和平台系统使用精度的关键因素。针对此问题,分析磁悬浮系统加力的作用机理,对系统的力学模型进行研究。从刚体动力学基本方程出发,以三浮陀螺浮子组件为研究对象,建立了浮子5个受控自由度的动力学关系和浮子运动的状态方程。然后对瞬时冲击力、阶跃常值力和简谐变化力作用下浮子运动规律的进行了分析和计算。仿真结果表明,当三种过载同时作用在浮子上时,磁悬浮系统在闭环状态下浮子位移的稳态值为2.12?m,即浮子最终停在线性区的边缘,不会碰到轴尖,因此不会影响仪表的精度和可靠性。但由于加力的刚度比较小,系统的过渡时间比较长。     

完全笛卡尔坐标描述的多体系统动力学

用完全笛卡尔坐标描述多体系统的运动学和动力学在提高计算效率方面有突出优点．导出用完全笛卡尔坐标表示的刚体及多体系统的动量和动量矩的解析式,给出与之对应的广义惯量矩阵概念,建立无力矩状态下用完全笛卡尔坐标描述的多体系统动力学的一阶微分方程组,用于多体航天器的姿态运动分析     

Screw-matrix method in dynamics of multibody systems

In the present paper the concept of screw in classical mechanics is expressed in matrix form, in order to formulate the dynamical equations of the multibody systems. The mentioned method can retain the advantages of the screw theory and avoid the shortcomings of the dual number notation. Combining the screw-matrix method with the tool of graph theory in Roberson/Wittenberg formalism. We can expand the application of the screw theory to the general case of multibody systems. For a tree system, the dynamical equations for eachj-th subsystem, composed of all the outboard bodies connected byj-th joint can be formulated without the constraint reaction forces in the joints. For a nontree system, the dynamical equations of subsystems and the kinematical consistency conditions of the joints can be derived using the loop matrix. The whole process of calculation is unified in matrix form. A three-segment manipulator is discussed as an example. This work is supported by the National Natural Science Fund.     

自旋液体晃动研究

对旋转对称中心贮箱内的自旋液体晃动问题,提出了一个直接对Ｅｕｌｅｒ方程进行Ｇａｌｅｒｋｉｎ离散的近似方法,并分析了方法的近似性。     

多刚体系统动力学的旋量-矩阵方法

本文将经典力学中的旋量概念以矩阵形式表示,用以建立多刚体系统的动力学方程。这种旋量-矩阵方法能保留旋量融矢量与矢量矩于一体的优点,却避免以往对偶数记法的缺点。结合 Roberson/wittenburg的图论工具,旋量-矩阵方法的应用范围可扩大到一般多刚体系统。对于树形系统,利用旋量通路矩阵推导各个由第i铰联结的全部外侧刚体组成的第i子系统的动力学方程,可避免出现铰的约束反力,对于非树系统,则利用回路矩阵导出各子系统动力学方程及运动学相容条件,全部计算过程统一为矩阵运算,以操作机器人作为具体算例。     

刚性椭球对固定面的三维摩擦碰撞

讨论刚性椭球对固定面的三维摩擦碰撞．以法向冲量为自变量,建立碰撞过程中接触点切向速度的微分方程．利用相平面的奇点理论对碰撞过程中切向滑动的全局性态作定性分析,并导出切向滑动的解析积分．     

Quasi-Euler-Poinsot motion of a rigid body

The phase-plane method of nonlinear oscillation is used to discuss the influence of the small dissipation upon the Euler-Poinsot motion of a rigid body about a fixed point. The equations of phase coordinates are applied instead of Eulerian equations, and the global characteristics of the motion of rigid body are analysed according to the distribution and the type of the singular points. A Chaplygin's sphere on a rough plane, a rigid body in viscous medium and one with a cavity filled with viscous fluid are discussed as examples. It is shown that the motions of rigid bodies dissipated by various physical factors have a common qualitative character. The rigid body tends to make a permanent rotation about the principal axis of the largest moment of inertia. The transitive process can change from oscillatory to aperiodic with the decrease in dissipation.     

鞍马全旋运动的动力学

本文从经典力学观点讨论人体在鞍马上的全旋运动,理想化的全旋运动要求人体以不变的章动角作匀速进动,同时绕纵轴朝相反方向自旋,以保证在运动过程中始终面向前方。文中规定一种带特殊完整约束条件的刚体规则进动作为这种运动的理想模式,并利用人体的多刚体模型分析鞍马上的直体全旋及托马斯全旋的运动规律,导出肩关节支撑力及肌肉控制力矩的计算公式。     

Melnikov's method for rigid bodies subject to small perturbation torques

Summary In this paper, the global motion of rigid bodies subjected to small perturbation torques, either conservative or dissipative, is investigated by means of Melnikov's method. Deprit's variables are introduced to transform the equations of motion into a standard form which is rendered suitable for the application of Melnikov's method. The Melnikov method is used to predict the transversal intersections of stable and unstable manifolds for the pertubed rigid-body motion. The chosen examples are a self-excited rigid body subject to a small periodic torque in a viscous medium, and the heavy rigid body. It is shown in both cases that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.     

硅微机械振动轮陀螺仪的机理研究

本文针对Ｄｒａｐｅｒ 实验室公布的硅微机械振动轮陀螺仪的设计方案,给出了它的非线性 动力学方程和运动规律,分析了该陀螺仪壳体绕空间任意轴匀速旋转时干扰力矩所引起的漂 移率,给出了比通常线性化处理后得到的角速率测量关系式更为精确的测量表达式。     

玻璃弹珠中的趣味动力学

用手去推倾斜的V形槽中排成一列的刚体小球,实验表明,小球的运动具有不稳定性,即初始球数为奇数时,第2个小球(从下向上数)会首先从V形槽中被挤出;而球数为偶数时,第3个小球会首先被挤出．对于这种有趣的现象,考虑接触间存在库仑摩擦,进行了数值模拟,得到了与实验完全一致的结果,并得到了小球转动的一些规律．最后根据实验以及数值模拟结果总结了小球被挤出难易程度与模型参数之间的一些关系．     

自旋液体晃动Pfeiffer方法的分析

本文对研究自旋液体晃动的Pfeiffer方法提出了一种分析方法,从而将液体自由振动的稳定性的Pfeiffer方法推广于既有重力又有自旋的液体晃动的研究。     

带充液腔重刚体的自旋稳定性

本文讨论带任意个充液腔的重刚体的自旋稳定性。以平均涡量作为液体的离散化变量,导出解析形式稳定性判据,并用于讨论充液自旋弹丸。对腔内隔板增强自旋稳定性的实际效果进行了估计。     

用灰色理论和神经网络理论建立陀螺漂移模型初探

本文就灰色理论和神经网络技术在建立陀螺漂移模型上的应用进行了初步探讨；介绍了这两种理论工程应用上的方法和特点以及相关的一些问题。     

Kirchhoff动力学比拟对弹性薄壳的推广

将弹性细杆的\"Kirchhoff动力学比拟\"方法推广到弹性薄壳,使弹性薄壳的变形在物理概念上和刚体的运动对应, 在数学表述上等同,从而可以用刚体动力学的理论和方法研究弹性薄壳的变形,为连续的弹性薄壳提供新的离散化方法. 在直法线假设下,在弹性中面上构筑空间正交轴系, 此轴系沿坐标线\"运动\"的角速度构成两自变量的弯扭度. 沿两个坐标线的弯扭度表达了弹性薄壳的变形和位形,证明了弯扭度之间以及弯扭度与中面切矢间的相容关系. 用Euler角和Lam$acute{e}$系数表达了非完整约束和中面位形的微分方程,用弯扭度和Lam$acute{e}$系数表达了应变和应力以及内力及其本构方程.导出了用分布内力集度表达的弹性薄壳在变形后位形上的平衡偏微分方程组,方程的形式与刚体动力学的Euler方程和弹性细杆的Kirchhoff方程具有相似性,实现了Kirchhoff动力学比拟对弹性薄壳的推广.总结了弹性薄壳静力学和刚体动力学以及弹性细杆静力学在概念上的比拟关系.最后给出了一个算例. 为研究弹性薄壳的变形和运动提供新的建模方法和研究思路.也可进一步推广到弹性薄壳动力学.