Preface
Chapter 1. INTRODUCTION TO DYNAMICS
1.1 Basic Concepts of Dynamics
1.2 Axioms of Dynamics
1.3 Systems of units
Chapter 2. EQUATIONS OF MOTION OF A PARTICLE
2.1 Differential equations of motion of a particle
2.1.5 Motion of a constrained particle
2.2 Equations of motion of a particle system
2.3 Static representation dynamic equations of a particle. D’Alembert’s principle
Chapter 3. MOMENTUM METHODS
3.1 Some definitions
3.2 Theorem of linear momentum
3.3 Theorem of Motion of Center of Mass
3.4 Moment of inertia of a body
3.5 Theorem of angular momentum
3.6 Equations of motion of a body rotation about a fixed axis
3.7 Equations of motion of a body in general plane motion
3.8 Equations of motion of a planar rigid body system
Chapter 4. ENERGY METHODS
4.1 Work of a force and a torque
4.2 Theorem of kinetic energy
4.3 Conservative Forces, Potential Energy and Conservation of Energy
Chapter 5. IMPACT
5.1 Concepts and assumptions
5.2 Impact of two translational bodies
5.3 Impact of a particle to body rotation about a fixed axis – Center of percussion
5.4 Impact of two bodies
Chapter 6. PRINCIPLE OF VIRTUAL WORK
6.1 Basic concepts of analytical mechanics
6.2 Principle of virtual work
6.3 Illustrative examples
6.4 Stability of an equilibrium state
Chapter 7. D'ALEMBERT'S PRINCIPLE
7.1 D’Alembert’s principle for a particle
7.2 D’Alembert’s principle for a mechanical system
7.3 Dynamics-Statics Methods
7.4 Illustrative examples
Chapter 8. D’ALEMBERT – LAGRANGE PRINCIPLE AND LAGRANGE’S EQUATION
8.1 D’Alembert – Lagrange principle
8.2 Lagrange Equations of the second Kind
8.3 Lagrange Equation with multipliers
Chapter 9. KINETICS OF RIGID BODIES IN THREE DIMENSIONS
9.1 Moment of inertia and product of inertia
9.2 Linear and angular momentum of a rigid body
9.3 Kinetic energy of a rigid body
9.4 Dynamic equations of a rigid body in three dimensions
9.5 Body rotation about a fixed axis – bearing reactions
9.6 Differential equations of motion for a body rotation about a fixed point
9.7 Gyroscopic motion – Approximate Theory of Gyroscope
9.8 Differential equations of motion of a rigid body in three dimensions
Chapter 10. MECHANICAL VIBRATIONS
10.1 Introduction
10.2 Vibration of single degree of freedom system
10.3 Vibration of multi degree of freedom systems
10.4 Mechanical-Electrical Analogy
Appendix A1. Some mathematical expressions
Appendix A2. Moment of inertia of homogeneous rigid bodies
Appendix A3. Some vector operations
References