动点选取法的剖析

本通过点的合成运动中动点系两种不同选法利弊的剖析,说明动点动系选取应该遵循的基本原则。     

动点的牵连运动分析与运动合成定理推证

点的合成运动分析中,复杂运动合理地分解和合成的关键在于牵连点的运动分析,牵连点是动系上与动点瞬时相重合的点,由于动点在动系上不断变迁,故牵连点随时间变动。本文指出,任一瞬时,牵连点均是动系上的某一“固定”点,仅随动系一起运动,采用解析方法提出了牵连点速度和加速度的一种表示方法,并推导了点的速度和加速度合成定理。本方法无需引入相对导数,易于学生理解。     

关于点的合成运动速度合成定理两种推导的辨析

针对И.М.伏龙科夫著的理论力学教材中点的合成运动速度合成定理推导,指出推导过程在概念上和数学上出现的错误. 并给出正确的推导过程,以引起力学教学工作者注意.     

刚体绕平行轴转动动量矩求解方法的分析

从``质点系相对其质心动量矩'的概念,分析了质点系相对其质心绝对动量矩等于其相对动量矩的满足条件. 从``刚体平面运动的合成'的概念得到一种新的求解方法:``${\pmb L}_{o} = {\pmb L}_e + {\pmb L}_{r}https://pubs.cstam.org.cn/article/doi/10.6052/1000-0992-2007-138https://pubs.cstam.org.cn/article/exportPdf?id=mie_137552刚体;平行轴;平面运动;牵连运动;质心http://d.wanfangdata.com.cn/Periodical_lxysj200805026.aspx塔里木大学农业工程学院周岭 http://lxsj.cstam.org.cn/CN/10.6052/1000-0992-2007-138塔里木大学农业工程学院1900-01-012008-10-10', 即刚体绕平行轴转动对某点绝对动量矩等于刚体作牵连运动对该点动量矩与刚体相对质心转动产生动量矩的矢量和,为学生较好理解``刚体绕平行轴转动动量矩'的求解提供了新思路.     

推导加速度合成公式的“牵连点跟踪法”1）

理论力学是大学工科各专业本科生的技术基础课,点的合成运动是重点与难点内容之一。部分学生对牵连（加）速度,特别是对（加）速度合成定理的推导需要较长时间才能理解和适应。很多教材（如文献[1,2]）都引入了“牵连点”的概念。牵连点的定义为：某瞬时与动点重合的动系上的点称为动点在该瞬时的牵连点。由于动点相对动系有运动,不同的瞬时动点与动系上不同的点重合,因此不同瞬时的牵连点是不同的。某瞬时的牵连（加）速度就是该瞬时的牵连点相对定系的（加）速度。牵连点的引入能较好地帮助学生理解牵连（加）速度。在定理推导的教学实践中,虽然用目前的教材中所采用的方法都能很好地证明该定理,但我们注意到,“两点”（即牵连点与动点）在时间点和空间位置上的“重叠性”会给学生带来理解和掌握的难度,学生容易在“重叠性”这一点上产生困惑。文献[3]就动系做定轴转动,采用了一种将动点从其重合点“拉开”的方式,对该定理进行了推导,对解决学生的困惑有一定帮助。以下,本文以文献[3]的方法为基础,补充引入“牵连点”、“绝对和相对导数”等重要概念,并就动系做一般运动对该定理进行推导,在表达方式上也做了一些调整。本文称这种推导方式为“牵连点跟踪法”。     

运动学中点的合成运动分析方法

本文就运动学中点的合成运动分析方法进行了梳理与研讨。采用广义坐标方法推导了动参考系作一般运动下点的速度与加速度合成公式,并与教材中的表达式进行了对比。此外还采用本文提出的基于牵连点运动的分析方法,对点的合成运动进行了详细的研究,并重点讨论了两种分析方法的特点与应用。

     

推导加速度合成公式的“牵连点跟踪法”

 在理论力学课程中关于点的合成运动的教学,可采用跟踪"牵连点" 的方式来推导(加) 速度合成定理. 即让某瞬时的牵连点与动点从空间位置上"分离",从定系和动系的原点,同时向动点和牵连点各引出两条矢径,跟踪牵连点任意时刻的运动. 然后将以上引出的四条矢径所满足的基本关系式对时间求导,即得到任意时刻的(加) 速度关系式. 再将牵连点的条件代入该(加) 速度关系式,可导出(加) 速度合成定理. 该推导方法概念明确、清晰,各物理量间具有较好的"可辨识性",便于学生理解和掌握.     

单机开式复合约束绳系吊装的动点坐标与绳力的通用程序算法分析

主要介绍单机开式复合约束绳系吊装计算的通用程序算法。利用Picard迭代法建立了单机开式复合约束绳系动点坐标的通用迭代算法,以及绳力计算的通用算式,并描述了实现通用算法的关键编程技术;典型算例结果分析表明,通用程序算法是非常有效的,Picard迭代法具有重要的工程应用价值。     

关于刚体角速度定义的一个注解

给出了一种角速度定义方法. 这种方法基于固连坐标系基矢量和单位矢量的导数给出,但避免使用角速度矩阵概念. 另外从刚体上速度分布的角度,用速度场旋度的方法解释角速度. 可以帮助学生从另外一个角度来理解角速度概念.     

On the motion of a mass point on a surface

The motion of a mass point (particle) on a smooth surface in a potential force field is considered. To determine the particle trajectories, Zhukovskii’s geometric approach[1] is elaborated. It is shown that the trajectory equations obtained by this method are equivalent to the trajectory equations which can be derived from the Lagrange equations by the isoenergetic reduction (Whittaker’s method [2]). The geometric approach enables one to prove that if the external forces are tangent to the particle trajectory (e.g., “dry friction” forces), then the trajectories coincide with the geodesics. This research extends the results obtained in [3].     

On the motion of a material point on a moving surface

Summary Sufficient conditions are given for the stability and instability of the equilibrium position x=y=z=0 in the mechanical system consisting of a material point constrained to move on the moving surface z=−λ(t)(x²+y²) (λ(t)>0) in a constant field of gravity (the axis 0z is directed vertically upward) under the action of viscous friction of total dissipation.

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Sommario Si danno condizioni sufficienti per la stabilità e la instabilità della posizione di equilibrio x=y=z=0 nel sistema meccanico che consiste di un punto materiale vincolato a muoversi sulla superficie mobile z=−λ(t)(x²+y²) (λ(t)>0) in un campo di gravità costante (l'asse 0z è diretto verticalmente e orientato verso l'alto) sotto l'azione di attriti viscosi con dissipazione completa.

     

On the motion of a heavy dynamically symmetric rigid body with vibrating suspension point

The motion of a dynamically symmetric rigid body in a homogeneous field of gravity is studied. One point lying on the symmetry axis of the body (the suspension point) performs high-frequency periodic or conditionally periodic vibrations of small amplitude. In the framework of approximate equations of motion obtained earlier, we find necessary and sufficient conditions for the stability of the body rotation about the vertical symmetry axis and study the existence and stability of regular precessions of the body in the coordinate system translationally moving together with the suspension point.     

On the rotational motion of a gyrostat about a fixed point with mass distribution

The perturbed rotational motion of a gyrostat about a fixed point with mass distribution near to Lagrange’s case is investigated. The gyrostat is subjected under the influence of a variable restoring moment vector, a perturbing moment vector, and a third component of a gyrostatic moment vector. It is assumed that the angular velocity of the gyrostat is sufficiently large, its direction is close to the axis of dynamic symmetry, and the perturbing moments are small as compared to the restoring ones. These assumptions permit us to introduce a small parameter. Averaged systems of the equations of motion in the first and second approximations are obtained. Also, the evolution of the precession angle up to the second approximation is determined. The graphical representations of the nutation and precession angles are presented to describe the motion at any time.     

点的复合运动中相对运动的描述

给出了点的复合运动中,动点的绝对运动方程和相对运动方程之间关系的描述方法,并将其应用于确定平面运动机构中选取不同动点和动系时的相对运动轨迹.该方法的推导过程简单易懂,易于实现,可以帮助学生在学习相关知识时对不同情况下的相对运动有清晰、直观的了解.特别是当相对运动非常复杂时,可以借助该分析过程给出相对运动轨迹曲线.     

Fluid motion in the stagnation point neighborhood

An analytical solution of the inviscid incompressible fluid equations (outer flow), which serves as the asymptote for the numerical solution of the viscous-fluid equations (inner flow), is presented. Using this solution, the effect of the spreading rate and the vorticity of the outer flow on the heat transfer (heat flux "peaks") can be studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 97–101, July–August, 2000.     

Serret-Andoyer变量描述的刚体定点运动

叙述刚体动力学中Serret-Andoyer变量的基本概念. 导出用其表达的刚体定点运动动力学方程,叙述其在航天器姿态动力学和陀螺力学中的应用.     

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.