《理论力学 Theoretical Mechanics——动力学》（双语版）第十五章 达朗伯原理 D'Alembert's principle

Theoretical Mechanics Chapter. Aterbets principle

Theoretical Mechanics

理论力学 第十五拿能原

Dynarnics An important theorem of dynamics, D Alembert's principle, will be introduced in this chapter. By this principle dynamical problems can be transformed formallyformally into those of statics. Then they can be solved by the theorem of equilibrium. Therefore this method to solve the dynamical problems of dynamics is called the dynamic- static method

3 An important theorem of dynamics, D’Alembert’s principle,will be introduced in this chapter. By this principle dynamical problems can be transformed formally formally into those of statics. Then they can be solved by the theorem of equilibrium. Therefore this method to solve the dynamical problems of dynamics is called the dynamic￾static method

学 本章介绍动力学的一个重要原理达朗伯原理。应用 这一原理,就将动力学问题从形式上转化为静力学问题,从 而根据关于平衡的理论来求解。这种解答动力学问题的方法, 因而也称动静法

4 本章介绍动力学的一个重要原理——达朗伯原理。应用 这一原理，就将动力学问题从形式上转化为静力学问题，从 而根据关于平衡的理论来求解。这种解答动力学问题的方法， 因而也称动静法

Chapter 15: D'Alembert's principle D8 15-1 The concept of the inertial force and the D'Alembert's principle for one particle §15-2D’ Alembert’ s principle for a system of particles $15-3 The simplification of a system of inertial forces of a rigid body $15-4 Dynamical reaction of the bearing of a rigid body under fixed-axis rotation and the concepts of static and dynamic equilibrium e The application of D' Alembert's principle

§15–1 The concept of the inertial force and the D’Alembert’s principle for one particle §15–2 D’Alembert’s principle for a system of particles §15–3 The simplification of a system of inertial forces of a rigid body §15–4 Dynamical reaction of the bearing of a rigid body under fixed-axis rotation and the concepts of static and dynamic equilibrium The application of D’Alembert’s principle Chapter 15: D'Alembert's principle

第十五章达朗伯原理 §15-1惯性力的概念·质点的达朗伯原理 §15-2质点系的达朗伯原理 §15-3刚体惯性力系的简化 四§15-4定轴转动刚体的轴承动反力 静平衡与动平衡的概念 达朗伯原理的应用

§15–1 惯性力的概念 · 质点的达朗伯原理 §15–2 质点系的达朗伯原理 §15–3 刚体惯性力系的简化 §15–4 定轴转动刚体的轴承动反力  静平衡与动平衡的概念 达朗伯原理的应用 第十五章 达朗伯原理

Dynamic 815-1 The concept of the inertial force and D'Alembert's principle for a particle 1. The concept of the inertial force If a man is pushing the cart by hands, then Q=-F=-ma he force@ comes from the inertia of the cart keep the force diagram as the original motion amar state, the reaction force to the object(hands) applying the force is called the inertial force of the cart Concept of the inertial force of a particle: h If a particle is moving accelerated, the sum of the inertial reactions of the particle to the objects which force it to produce the accelerated motion is called the inertial force of the particle 7

7 §15-1 The concept of the inertial force and D’Alembert’s principle for a particle If a man is pushing the cart by hands, then Q = −F = −ma The force comes from the inertia of the cart, keep the force diagram as the original motion state, the reaction force to the object (hands) applying the force is called the inertial force of the cart. Q Concept of the inertial force of a particle: If a particle is moving accelerated, the sum of the inertial reactions of the particle to the objects which force it to produce the accelerated motion is called the inertial force of the particle. Q = −ma 1. The concept of the inertial force

§15-1惯性力的概念·质点的达朗伯原理 、惯性力的概念 人用手推车F=-F=-ma F 力F是由于小车具有惯性,力图保持原来 F 的运动状态,对于施力物体(人手)产生的 反抗力。称为小车的惯性力。 定义:质点惯性力 =-h 加速运动的质点,对迫使其产生加速运动的物体的惯 性反抗的总和

8 §15-1 惯性力的概念 · 质点的达朗伯原理 人用手推车 F' = −F = −ma 力 是由于小车具有惯性，力图保持原来 的运动状态，对于施力物体(人手)产生的 反抗力。称为小车的惯性力。 F' 定义：质点惯性力 加速运动的质点，对迫使其产生加速运动的物体的惯 性反抗的总和。 Q = −ma 一、惯性力的概念

Dynarnics o--mnam Q2=-ma1=-m= Oy=-ma, dy Q,=-ma,=-m ma =m2 Oh==ma,=Oo notice The inertial force is not the real force acting on the particle, it is the resultant force of reaction of the particle to the object applying the force

9 2 。 2 2 2 2 2 , , dt d z Q ma m dt d y Q ma m dt d x Q ma m z z y y x x = − = − = − = − = − = − 0。 , , 2 2 2 = − = = − = − = − = − b b n n Q ma v Q ma m dt d s Q ma m    [notice] The inertial force is not the real force acting on the particle, it is the resultant force of reaction of the particle to the object applying the force

2x=-max=-m,2 @=-ma,=-ma-s dt2 o.-ma. v Q O Q2=-ma2=-m 2b=-mab=0 注]质点惯性力不是作用在质点上的真实力,它是质点对施 力体反作用力的合力。 10

10 2 2 2 2 2 2 dt d z Q ma m dt d y Q ma m dt d x Q ma m z z y y x x = − = − = − = − = − = − 0 2 2 2 =− = =− =− =− =− b b n n Q ma v Q ma m dt d s Q ma m    [注] 质点惯性力不是作用在质点上的真实力，它是质点对施 力体反作用力的合力