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## Volume 3: Theoretical Mechanics

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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

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1st Edition - January 1, 1963

Authors: Brian H. Chirgwin, Charles Plumpton

Language: EnglisheBook ISBN:

9 7 8 - 1 - 4 8 3 1 - 8 4 5 1 - 7

A Course of Mathematics for Engineers and Scientists, Volume 3: Theoretical Mechanics details the fundamentals concepts of theoretical mechanics. The title first covers the… Read more

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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.

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

- No. of pages: 382
- Language: English
- Edition: 1
- Published: January 1, 1963
- Imprint: Pergamon
- eBook ISBN: 9781483184517

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