Lecture Notes on Theoretical Mechanics

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普通高等教育“十三五”规划教材

内容简介

本教材首先回顾了本科生必备掌握的平面几何和空间几何的基本知识，然后补充了向量运算等内容。主要内容分为静力学、运动学和动力学三部分。其中静力学为主要部分，主要阐述了力系的简化和平衡、平面一般力系等内容。运动学以讲授刚体的平面运动为主。动力学部分阐述了动量、动量矩、动能等三大定理。

目录

1 Preliminary Knowledge

1.1 Trigonometric Function

1.2 Concept of Distance

1.3 Scalar and Vector

Exercises

Part I Statics

2 Fundamentals of Statics

2.1 Force

2.2 Axioms in Statics

2.3 Moment of a Force

Exercises

3 Force Analysis

3.1 Constraint

3.2 Force Analysis

Exercises

4 Simplification of a Force Group

4.1 Planar Couple

4.2 Theorem of Parallel Translation of a Force

4.3 Simplification of a Force System

4.4 Further Simplification of a Force System

Exercises

5 Equilibrium of the General Coplanar Force Group

5.1 Equilibrium Equations for One Rigid Body System

5.2 Rigid Multi-body System

Exercises

6 Center of the Parallel Force Group

6.1 Theorem of the Resultant Moment

6.2 Center of the Parallel Force System

6.3 Gravitational Center

Exercises

Part II Kinematics

7 Motion of a Particle

7.1 Cartesian Coordinate System

7.2 Natural Coordinate System

Exercises

8 Basic Motion of the Rigid Body

8.1 Translation

8.2 Rotation on a Fixed Axis

Exercises

9 Planar Motion of the Rigid Body

9.1 Relative Velocity

9.2 Instantaneous Center

Exercises

Part III Kinetics

10 Newton’s Laws of Motion

Exercises

11 Theorem of Momentum

Exercises

12 Theorem of Angular Momentum

12.1 Moment of Inertia of a Rigid Body to an Axis

12.2 Theorem of Angular Momentum

Exercises

13 Theorem of Kinetic Energy

13.1 Work

13.2 Kinetic Energy

13.3 Theorem of Kinetic Energy

Exercises

14 Lagrange Equation

Exercises

Contents15 Summary

15.1 Similar Examples in Nature

15.2 Analogies in Theoretical Mechanics

References