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Applied Mechanics Dynamics

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TOC

I. THE GENERAL PRINCIPLES OF DYNAMICS
1.1. The Laws of Motion
1.2. Definitions
1.3. Frames of Reference
1.4. Fundamental and Derived Units
1.5. Dimensions
1.6. Dimensional Homogeneity
1.7. Dimensional Analysis
1.8. The Theory of Models

II. KINEMATICS : THE DESCRIPTION OF MOTION
2.1. Displacement, Velocity, and Acceleration
2.2. Angular Velocity
2.3. Motion Referred to a Moving Coordinate System

III. DYNAMICS OF A PARTICLE
3.1. Integration of the Equation of Motion for Particular Problems
3.2. The Equation of Impulse and Momentum
3.3. The Equation of Work and Energy
3.4. Potential
3.5. Potential Energy
3.6. The Conservation of Energy
3.7. The Solution of Problems in Dynamics

IV. APPLICATIONS OF PARTICLE DYNAMICS
4.1. The Motion of a Body Falling Through a Resisting Medium
4.2. Projectile Motion
4.3. Planetary Motion
4.4. Impact
4.5. The Scattering of Particles
4.6. The Pressure in a Gas
4.7. Variable Mass Systems
4.8. Jet Propulsion Problems
4.9. Electron Dynamics
4.10. The Acceleration of Electrons
4.11. The Cathode-Ray Oscilloscope
4.12. The Equivalence of Mass and Energy

V. DYNAMICS OF VIBRATING SYSTEMS
5.1. The Vibration Problem
5.2. The Characteristics of the Forces
5.3. The Differential Equation of the Vibration Problem
5.4. Free Vibrations of an Undamped System
5.5. Damped Vibrations
5.6. Forced Vibrations
5.7. Vibration Isolation
5.8. The Design of Vibration Measuring Instruments
5.9. Vibrations with Non-periodic Forces
5.10. Oscillations in Electric Circuits

VI. PRINCIPLES OF DYNAMICS FOR SYSTEMS OF PARTICLES
6.1. The Equation of Motion for a System of Particles
6.2. The Motion of the Center of Mass
6.3. The Total Kinetic Energy of a System of Particles
6.4. Moment of Momentum
6.5. Summary

VII. THE DYNAMICS OF RIGID BODIES
7.1. Kinematics of Rigid Body Motion
7.2. The Moment of Momentum of a Rigid Body
7.3. Moments and Products of Inertia
7.4. The Calculation of Moments and Products of Inertia
7.5. Translation of Coordinate Axes
7.6. Rotation of Coordinate Axes
7.7. Principal Axes
7.8. The General Equations of Motion for a Rigid Body
7.9. Equations of Motion for a Translating Body
7.10. The Rotation of a Rigid Body About a Fixed Axis
7.11. Plane Motion of a Rigid Body
7.12. Rotation About a Fixed Point
7.13. The Symmetrical Top and the Gyroscope
7.14. The Gyroscopic Compass
7.15. General Motion in Space. Rolling of a Disk
7.16. Stability of Rigid Body Motion. The Rolling Disk
7.17. D’Alembert’s Principle

VIII. NON-RIGID SYSTEMS OF PARTICLES
8.1. Longitudinal Waves in an Elastic Bar
8.2. The Traveling Wave Solution
8.3. The Longitudinal Vibrations of a Bar
8.4. The Equations of Motion of a Non-viscous Fluid
8.5. The Energy Equation
8.6. Bernoulli’s Equation by Euler’s Method
8.7. The Momentum Equation
8.8. The Momentum Equation for an Accelerating Volume

IX. ADVANCED METHODS IN DYNAMICS
9.1. Generalized Coordinates
9.2. Lagrange’s Equations for a Particle
9.3. Lagrange’s Equations for a System of Particles
9.4. Oscillations of Two Degree of Freedom Systems
9.5. Principal Modes of Vibration
9.6. Small Oscillations of a Conservative System
9.7. The Potential Energy Function
9.8. The Kinetic Energy Function
9.9. The General Equations of Free Oscillations
9.10. Orthogonality of the Principal Modes
9.11. Example: The Calculation of Natural Frequencies and Mode Shapes
9.12. Forced Oscillations
9.13. The Calculus of Variations
9.14. Euler’s Differential Equation
9.15. Hamilton Principle
9.16. Hamilton’s Canonical Equations of Motion

APPI. BIBLIOGRAPHY
11. UNITS OF MASS AND FORCE
111. VECTOR PRODUCTS
IV. PROPERTIES OF PLAN SECTIONS
PROPERTIES OF HOMOGENEOUS BODIES
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