A Course of Mathematics for Engineers and Scientists

A Course of Mathematics for Engineers and Scientists

Volume 3: Theoretical Mechanics

1st Edition - January 1, 1963

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  • Authors: Brian H. Chirgwin, Charles Plumpton
  • eBook ISBN: 9781483184517

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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


    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


    Chapter IV. Kinematics


    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


    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


    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


    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


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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