关于牛顿力学的力和拉格朗日力学的力------理论力学札记之九

讨论了牛顿力学和拉格朗日力学中的力. 在牛顿力学中着重讨论了主动力, 约束和理想约束力. 在拉格朗日力学中着重讨论了广义力的两种分解方法.     

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.     

关于动量守恒律和动量矩守恒律 --理论力学札记之二

介绍质点系对任意动轴的动量守恒律和动量矩守恒律，并举例说明对完整和非完整系统的应用．     

关于达朗贝尔原理------理论力学札记之六

介绍d'Alembert原理的原述, 后人对d'Alembert原理的理解, 并给出几点评论.     

质系动量矩定理应用二例

设计了两个应用质系动量矩定理的例子. 表面上看,它们似乎违反常识; 实际上, 它们都符合科学, 而且能加深对质系动量矩定理的理解.     

魔术的力学分析之二------四连环与莫尔定理

对``四连环'可表演的各种图案,莫尔定理简述,有缺口钢环张开量的计算公式的推导$^{[1]}$, 并从公式导出的结果讨论了钢环张开量与一些参数的关系,并进行了实验测试,这样,可以让人们认识这个魔术教具也是力学的应用.     

关于“动矩心”的几种动量矩定理的一致性

1.引言取任意“动点”为矩心的几种动量矩定理在理论力学教科书中均有不同程度的介绍,其等价性已在理论上得到解决.然而在实际应用中,却导致了不正确的结果.由此引起了对应用“动矩心”的动量矩定理是否应附加条件的考察和争鸣.五十年代以来,我国有较多的文章研究这一问题,主要集中在平面运动     

《理论力学》学习中常见错误分析之一──动量矩定理的应用

《理论力学》学习中常见错误分析之一──动量矩定理的应用谢正桐,杨海兴（上海交通大学,上海２０００３０）本文根据一道具体习题的求解过程,指出动量矩定理应用中一个应注意的问题：不论是对定点还是对动点,应用动量矩定理必须取一般点而不能取特殊点。习题质量为ｍ...     

关于理想约束和虚位移原理——分析力学札记之二十

 理想约束是分析力学的基本假定, 虚位移原理是分析静力学的基本原理. 本文从经典著作和重要教材中提取一些信息, 期望描述理想约束和虚位移原理的形成和发展, 并发表一些议论.     

推导柯尼希定理和平行轴定理的一种新方法

针对定点运动刚体,利用动量定理、对固定点和质心的动量矩定理推导了柯尼希定理;针对平面运动刚体,利用动量定理和对动点的动量矩定理,推导了平行轴定理. 给出与以往教材不同的推导方法,并从两个方面推广了文献的结果. 从不同角度进行理论推导,可以帮助我们理解物理量、物理定律(定理)之间的联系,提高对物理本质的认识水平.     

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.

---

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.

     

Galin's theorem holds for moving punch

This paper presents a formulation for solving three-dimensional moving punch problem. It proves that Galin's theorem holds for the punch. As an example, the study offers some results (including numerical data) of dynamic displacement over an ellipse contact region.     

MINIMAX THEOREM AND SADDLE POINT THEOREM WITHOUT LINEAR STRUCTURE

I.IntroductionFanKyinequalityisaveryusefultoolinnoolinearanalysiswhichasserts:LetXbeanonemptycompactconvexsetinatopologicallinearspaceandWbeareal-valuedfunctiondefinedonXxX.Assumethat(i)9(x,y)islowersemicontinuousinac;(n)9(x,y)isquasiconcaveiny.ThenthereisboaXsuchthatsHPg(xo'Y)$sZPp(x,x).SinceFanKyprovedtheinequalityin1972,variousg...,.li..tlon,havebeen;v..byseveralauthors(see[l-3]andreferencestherein).Thepreviousgeneralizationsallremainedtheconditions(i)-'9(x,y)beinglowersemicontinuous…     

Dynamics of a satellite carrying a point mass moving about it

We study the dynamics of a complex system consisting of a solid and a mass point moving according to a prescribed law along a curve rigidly fixed to the body. The motion occurs in a central Newtonian gravitational field. It is assumed that the orbit of the system center of mass is an ellipse of arbitrary eccentricity.We obtain equations that describe the motion of the carrier (satellite) about its center of mass. In the case of a circular orbit, we present conditions that should be imposed on the law of the relative motion of the mass point carried by the satellite so that the latter preserves a constant attitude with respect to the orbital coordinate system. In the case of a dynamically symmetric satellite, we consider the problem of existence of stationary and nearly stationary rotations for the case in which the carried point moves along the satellite symmetry axis.We consider several problems of dynamics of the satellite plane motion about its center of mass in an elliptic orbit of arbitrary eccentricity. In particular, we present the law of motion of the carried point in the case without eccentricity oscillations and study the stability of the satellite permanent attitude with respect to the orbital coordinate system.