1 Motion of a Point Mass

1.1 Kinematics

1.1.1 Velocity and Acceleration

1.1.2 Velocity and Acceleration in Cartesian Coordinates

1.1.3 Rectilinear Motion

1.1.4 Planar Motion, Polar Coordinates

1.1.5 Three-Dimensional Motion, Serret-Frenet Frame

1.2 Kinetics

1.2.1 Newton’s Laws

1.2.2 Free Motion, Projectiles

1.2.3 Constrained Motion

1.2.4 Resistance/Drag Forces

1.2.5 Impulse Law and Linear Momentum, Impact

1.2.6 Angular Momentum Theorem

1.2.7 Work-Energy Theorem, Potential Energy, Conservation of Energy

1.2.8 Universal Law of Gravitation, Planetary and Satellite Motion

1.3 Supplementary Examples

1.4 Summary

2 Dynamics of Systems of Point Masses

2.1 Fundamentals

2.2 LinearMomentumfor a System of Point Masses

2.3 Angular Momentum Theorem for a System of PointMasses

2.4 Work-Energy Theorem and Conservation of Energy for a Systemof PointMasses

2.5 Central Impact

2.6 Bodies with VariableMass

2.7 Supplementary Examples

2.8 Summary

3 Dynamics of Rigid Bodies

3.1 Kinematics

3.1.1 Translation

3.1.2 Rotation

3.1.3 General Motion

3.1.4 Instantaneous Center of Rotation

3.2 Kinetics of the Rotation about a Fixed Axis

3.2.1 Principle of Angular Momentum

3.2.2 Mass Moment of Inertia

3.2.3 Work, Energy, Power

3.3 Kinetics of a Rigid Body in Plane Motion

3.3.1 Principles of Linear and Angular Momentum

3.3.2 Impulse Laws, Work-Energy Theorem and Conservation of Energy

3.3.3 Eccentric Impact

3.4 Kinetics of a Rigid Body in Three DimensionalMotion

3.4.1 Principles of Linear and Angular Momentum

3.4.2 Angular Momentum, Inertia Tensor, Euler’s Equations

3.4.3 Support Reactions in Plane Motion

3.4.4 The Torque-Free Gyroscope

3.5 Supplementary Examples

3.6 Summary

4 Principles of Mechanics

4.1 Formal Reduction of Kinetics to Statics

4.2 D’Alembert’s Principle

4.3 Lagrange Equations of the 2nd Kind

4.4 Supplementary Examples

4.5 Summary

5 Vibrations

5.1 Basic Concepts

5.2 Free Vibrations

5.2.1 Undamped Free Vibrations

5.2.2 Spring Constants of Elastic Systems

5.2.3 Damped Free Vibrations

5.3 Forced Vibrations

5.3.1 Undamped Forced Vibrations

5.3.2 Damped Forced Vibrations

5.4 Systems with two Degrees of Freedom

5.4.1 Free Vibrations

5.4.2 Forced Vibrations

5.5 Supplementary Examples

5.6 Summary

6 Non-Inertial Reference Frames

6.1 Kinematics of RelativeMotion

6.1.1 Translating Reference Frames

6.1.2 Translating and Rotating Reference Frames

6.2 Kinetics of RelativeMotion

6.3 Supplementary Examples

6.4 Summary

7 Numerical Simulation

7.1 Introduction

7.2 First-Order Initial-ValueProblems

7.3 Second-Order Initial-Value Problems

7.4 Supplementary Examples

7.5 Summary
Appendix
A Numerical Integration
index