Overview

This textbook covers a first course in mechanics on an applied mathematics degree course. Mechanics is introduced here in terms of the motion of a moving particle, with rigid body problems left until the subject is more fully developed. Full treatment of vectors, kinematics and dynamics is given as a precursor to specific discussions of topics in mechanics. Chapter 1 deals with the elementary theory of vectors and assumes limited prior knowledge of vector algebra. The mechanics of a particle is introduced in Chapters 2-8 inclusively, covering aspects such as resisting forces, work and energy, oscillations, central forces including Kepler's law and systems of particles. Chapter 9 is devoted to a full discussion of angular vectors including the theory of rotating axes, and Chapter 10 deals with the theory of moments as required for a full understanding of rigid body mechanics. These two chapters are used in developing the equations of motion as discussed in Chapter 11. The bulk of Chapter 11 is devoted to worked examples in order to demonstrate the many and varied applications of the equations of motion. Both 2- and 3-dimensional applications are discussed. Virtual work and Lagrange's equations are introduced in Chapter 12, and Chapter 13 describes some important techniques used in non-linear mechanics. Illustrative examples are provided throughout each chapter, and a substantial number of exercises is given at the end of each chapter. This book should be of interest to first year degree students in mathematics and applied mathematics.

Full Product Details

Author:   W. Chester
Publisher:   Chapman and Hall
Imprint:   Chapman and Hall
Edition:   Softcover reprint of the original 1st ed. 1979
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   0.688kg
ISBN:  

9780412439407

ISBN 10:   0412439409
Pages:   400
Publication Date:   31 December 1979
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Vectors.- 1.1 Introduction.- 1.2 Definitions.- 1.3 The Rules of Vector Algebra.- 1.4 The Resolution of a Vector.- 1.5 The Products of Vectors.- 1.6 The Derivative of a Vector.- 1.7 The Integral of a Vector.- 1.8 Scalar and Vector Fields.- 1.9 Line Integrals.- 1.10 The Gradient Operator.- 1.11 Equipotentials and Field Lines.- Exercises.- 2. Kinematics.- 2.1 Introduction.- 2.2 Velocity and Acceleration.- 2.3 Constant Acceleration.- 2.4 Projectiles.- 2.5 Dimensions.- Exercises.- 3. Dynamics.- 3.1 Newton's Laws.- 3.2 Units.- 3.3 Applications.- Exercises.- 4. Resisting Forces.- 4.1 Solid Friction.- 4.2 Motion through a Fluid.- Exercises.- 5. Impulse, Momentum, Work and Energy.- 5.1 Impulse and Momentum.- 5.2 Work and Energy.- 5.3 Potential Energy.- 5.4 Power.- Exercises.- 6. Oscillations.- 6.1 Simple Harmonic Oscillations.- 6.2 Damped Oscillations.- 6.3 Forced Oscillations.- 6.4 Coupled Oscillations.- 6.5 Non-Linear Oscillations.- Exercises.- 7. Central Forces.- 7.1 Basic Equations.- 7.2 Conservative Forces.- 7.3 Circular Orbits and Stability.- 7.4 Elliptic Harmonic Motion.- 7.5 The Inverse Square Law.- 7.6 Kepler's Laws.- 7.7 The Effect of Resistance.- Exercises.- 8. Systems of Particles.- 8.1 Mass Centre.- 8.2 Equations of Motion.- 8.3 Collision Problems.- 8.4 Variable Mass Problems.- Exercises.- 9. Angular Vectors.- 9.1 Existence.- 9.2 Angular Velocity.- 9.3 Relative Angular Velocity.- 9.4 Rotating Axes.- 9.5 Axes on the Earth's Surface.- Exercises.- 10. Moments.- 10.1 First Moment.- 10.2 Second Moment.- 10.3 Vector Moment.- 10.4 Parallel Vectors.- 10.5 Reduction of a System of Line Vectors.- 10.6 Work of a System of Line Vectors.- Exercises.- 11. Rigid Bodies.- 11.1 Equations of Motion.- 11.2 Impulse and Momentum.- 11.3 Work and Energy.- 11.4 Oscillations.- 11.5 Three-Dimensional Problems.- 11.6 Gyroscopic Problems.- Exercises.- 12. Virtual Work and Lagrange's Equations.- 12.1 Virtual Work.- 12.2 Generalised Coordinates.- 12.3 Lagrange's Equations.- 12.4 The Lagrangian and Hamiltonian.- Exercises.- 13. Non-Linear Problems.- 13.1 Conservative Forces.- 13.2 Autonomous Forces.- 13.3 The Method of Averaging.- 13.4 Forced Non-Linear Oscillations.- Exercises.

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