A Course of Mathematics for Engineers and Scientists
Volume 3: Theoretical Mechanics
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A Course of Mathematics for Engineers and Scientists, Volume 3: Theoretical Mechanics details the fundamentals concepts of theoretical mechanics. The title first covers the foundations of mechanics, and then proceeds to tackling plane statics and virtual work. Next, the selection talks about continuously distributed forces. The text also deals with kinematics, along with particle dynamics. Chapter VII covers systems of particles, while Chapter VIII tackles the uniplanar motion of a rigid body. The ninth chapter discusses stability, and the last chapter details impulsive motion and variable mass. The book will be of great use to students of engineering and pure and applied mathematics.
Table of Contents
Chapter I. The Foundations of Mechanics
Introduction
Fundamental Concepts
Newton's Laws of Motion
Chapter II. Plane Statics and Virtual Work
The Equilibrium of a Particle and a Rigid Body
Equivalent Sets of Forces
The Work Done by a Force
The Principle of Virtual Work
Potential Energy
Statically Indeterminate Systems
Chapter III. Continuously Distributed Forces
A Uniform, Flexible, Inelastic String Hanging under Gravity
Variable Loading - The Suspension Bridge
The Equilibrium of Heavy Elastic Strings
Strings in Contact with Surfaces
Shearing Forces and Bending Moments
The Bending of Thin Elastic Beams
Pure Flexure
The Properties of the Heaviside Unit Function and Its Derivative
Macaulay's Method
Clapeyron's Theorem of Three Moments
Struts
Chapter IV. Kinematics
Introduction
Velocity and Acceleration
Special Representations
The Hodograph
Relative Motion
Angular Velocity
Instantaneous Center: Centrodes
Chapter V. Particle Dynamics I: Motion with One Degree of Freedom
Introduction; Conservative Forces
Motion on a Straight Line
Simple Harmonic Motion and Damping
Motion in a Circle
Motion on Other Curves
Chapter VI. Particle Dynamics II: Motion with Two Degrees of Freedom
Introduction
The Motion of a Projectile in a Resisting Medium
Motion under a Central Force - General Theorems
The Differential Equations of Central Orbits
The Direct Law of Force
The Inverse Square Law
Newton's Theorem of the Revolving Orbit
Chapter VII. Systems of Particles
The Motion of Two Interacting Particles
The Encounter of Two Interacting Particles
The Motion of Connected Particles
The General Theory of Systems of Particles
The Motion of a Rigid Lamina
Applications of the Principles of Conservation of Linear Momentum, Angular Momentum and Energy to the Motion of Rigid Bodies
Moments and Products of Inertia of a Plane System
Chapter VIII. The Uniplanar Motion of a Rigid Body
Introduction
The Motion of a Rigid Body about a Fixed Axis
Systems without a Fixed Axis of Rotation
Conservative Systems of Force
Rolling and Sliding Motion
The Use of the Instantaneous Center: Initial Motions
Chapter IX. Stability
The Concept of Stability
Stability of Equilibrium
Oscillations about Stable Equilibrium
Motion on a Rotating Curve
Perturbation of an Orbit
Systems with More than One Degree of Freedom
Chapter X. Impulsive Motion and Variable Mass
Introduction
The Impulsive Motion of a System of Particles
Collisions between Particles
Collisions Between Bodies: Energy Changes
The Motion of a Body with Changing Mass - Rockets
Answers to the Exercises
Index
Product details
- No. of pages: 382
- Language: English
- Copyright: © Pergamon 1963
- Published: January 1, 1963
- Imprint: Pergamon
- eBook ISBN: 9781483184517
About the Authors
Brian H. Chirgwin
Charles Plumpton
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