Theoretical mechanics Part3: ) namics
1 Theoretical Mechanics
理论力学
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Dynamic Introduction 1. The subject of dynamics is the relation between the mechanical motion of a material body and the force acting on it 2 Two models of mechanics 1)A particle is a material body possessing mass, the shape and size of which can be neglected in investigating its motion Examples: When we study a satellites orbit the satellite may be regarded as a particle I. e, satellite- particle a rigid body in translation motion can al ways be treated as a particle I. e, rigid be oay particle 2)A system of particles is a collection of material points in which the position and motion of each particle of the system depends on the position and motion of all the other particles a rigid body is a special system of particles composed of a large number of particles, the distance between any two points of which remains the same during the whole motion. It is also called to be a non-deformable system 3
3 Introduction 1. The subject of dynamics is the relation between the mechanical motion of a material body and the force acting on it. 2. Two models of mechanics. 1) A particle is a material body possessing mass, the shape and size of which can be neglected in investigating its motion. Examples: When we study a satellite’s orbit the satellite may be regarded as a particle. I.e,satellite particle. A rigid body in translation motion can always be treated as a particle. I.e,rigid body particle. 2) A system of particles is a collection of material points in which the position and motion of each particle of the system depends on the position and motion of all the other particles. A rigid body is a special system of particles composed of a large number of particles, the distance between any two points of which remains the same during the whole motion. It is also called to be a non-deformable system
学 引言 一研究对象:研究物体的机械运动与作用力之间的关系 二力学模型: 1质点:具有一定质量而不考虑其形状大小的物体。 例如:研究卫星的轨道时,卫星质点; 刚体作平动时刚体一质点。 2质点系:由有限或无限个有着一定联系 的质点组成的系统。 刚体是一个特殊的质点系,由无数个相互间保持距离 不变的质点组成。又称为不变质点系
4 引 言 一.研究对象： 二.力学模型： 研究物体的机械运动与作用力之间的关系 2.质点系：由有限或无限个有着一定联系 的质点组成的系统。 1.质点：具有一定质量而不考虑其形状大小的物体。 刚体是一个特殊的质点系，由无数个相互间保持距离 不变的质点组成。又称为不变质点系。 例如： 研究卫星的轨道时，卫星 质点； 刚体作平动时,刚体 质点
Dynarnics System of free particles: a system in which the motion of each particle is not restricted by any constraints System of non-free particles refers to a system in which the motion of particle is restricted by constraints A system of particles is the most general abstract model of mechanics including rigid bodies, elastic bodies and fluids Particles dynamics Particle dynamics is the basis of the Dynamics of a system of particles dynamics of a system of particles 4. The fundamental problems of dynamics There are two cases in general. One is to determine the acting forces when the condition of motion is known, the other is to determine the motion of the body when the acting forces are known There are still some additional comprehensive problems. Sometimes part of the forces and part of the motion are known, we have to determine the other part In some cases, the positive forces are known, we should determine the motion firstly, then determine the reaction forces of constraints
5 System of free particles: a system in which the motion of each particle is not restricted by any constraints. System of non-free particles refers to a system in which the motion of particle is restricted by constraints. A system of particles is the most general abstract model of mechanics including rigid bodies, elastic bodies and fluids. 3. Classification of dynamics: Particles dynamics Particle dynamics is the basis of the Dynamics of a system of particles dynamics of a system of particles 4. The fundamental problems of dynamics: There are two cases in general. One is to determine the acting forces when the condition of motion is known, the other is to determine the motion of the body when the acting forces are known. There are still some additional comprehensive problems. Sometimes part of the forces and part of the motion are known, we have to determine the other part. In some cases, the positive forces are known, we should determine the motion firstly, then determine the reaction forces of constraints.
力单 自由质点系:质点系中各质点的运动不受约束的限制。 非自由质点系:质点系中的质点的运动受到约束的限制。 质点系是力学中最普遍的抽象化模型;包括刚体,弹性体,流体。 三动力学分类质点动力学 质点动力学是质点 质点系动力学系动力学的基础。 四动力学的基本问题:大体上可分为两类: 第一类:已知物体的运动情况,求作用力; 第二类:已知物体的受力情况,求物体的运动。 综合性问题:已知部分力,部分运动求另一部分力、部分运动。 已知主动力,求运动,再由运动求约束反力
6 自由质点系：质点系中各质点的运动不受约束的限制。 非自由质点系：质点系中的质点的运动受到约束的限制。 质点系是力学中最普遍的抽象化模型；包括刚体,弹性体,流体。 三.动力学分类: 质点动力学 质点系动力学 质点动力学是质点 系动力学的基础。 四.动力学的基本问题：大体上可分为两类： 第一类：已知物体的运动情况，求作用力； 第二类：已知物体的受力情况，求物体的运动。 综合性问题：已知部分力，部分运动求另一部分力、部分运动。 已知主动力，求运动，再由运动求约束反力
Theoretical mechanics Equations of Mochon of a Particle 7
7 Theoretical Mechanics
理论力学 算个一分
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Chapter 11: Differential equations of motion of a particle 8 11-1 The differential equations of motion of a particle 8 11-2 The two types of problems of particle dynamics
9 §11–1 The differential equations of motion of a particle §11–2 The two types of problems of particle dynamics Chapter 11: Differential equations of motion of a particle
第十一章质点运动微分方程 §11-1质点运动微分方程的形式 囚§811-2质点动力学两类问题
10 §11–1 质点运动微分方程的形式 §11–2 质点动力学两类问题 第十一章 质点运动微分方程