A First Course in Rational Continuum Mechanics - 1st Edition - ISBN: 9780127013015, 9781483220482

A First Course in Rational Continuum Mechanics

1st Edition

General Concepts

Authors: C. Truesdell
Editors: Samuel Eilenberg Hyman Bass
eBook ISBN: 9781483220482
Imprint: Academic Press
Published Date: 28th January 1977
Page Count: 304
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Description

A First Course in Rational Continuum Mechanics, Volume 1: General Concepts describes general concepts in rational continuum mechanics and covers topics ranging from bodies and forces to motions and energies, kinematics, and the stress tensor. Constitutive relations are also discussed, and some definitions and theorems of algebra, geometry, and calculus are included. Exercises and their solutions are given as well.

Comprised of four chapters, this volume begins with an introduction to rational mechanics by focusing on the mathematical concepts of bodies, forces, motions, and energies. Systems that provide possible universes for mechanics are described. The next chapter explores kinematics, with emphasis on bodies, placements, and motions as well as other relevant concepts like local deformation and homogeneous transplacement. The book also considers the stress tensor and Cauchy's fundamental theorem before concluding with a discussion on constitutive relations.

This monograph is designed for students taking a course in mathematics or physics.

Table of Contents


Preface


Contents of Future Volumes


Part 1 General Concepts


Chapter I Bodies, Forces, Motions, and Energies


1. Rational Mechanics


2. Bodies in General


3. Examples of Universes


4. Mass


5. Force


6. The Event World. Framings


7. Motions


8. Linear Momentum. Rotational Momentum. Kinetic Energy. Working. Torque


9. Changes of Frame


10. Rigid Motion


11. Frame-Indifference


12. Axioms of Mechanics


13. The Axioms of Inertia.


14. Euler's Laws of Motion Energy


General References


Chapter II Kinematics


1. Bodies, Placements, Motions


2. Mass-Density


3. Reference Placement. Transplacement


4. Descriptions of Motion


5. Local Deformation


6. Material Time Rates and Gradients in the Spatial Description. Material Surfaces. Kinematic Boundaries


7. Change of Reference Placement


8. Present Placement as Reference


9. Stretch and Rotation


10. Histories


11. Stretching and Spin


12. Homogeneous Transplacement


13. Rates of Change of Integrals Over Material Lines, Surfaces, and Regions. Material Vector Lines. The Vorticity Theorems of Helmholtz and Kelvin


14. Changes of Frame. Frame-Indifference


General References


Chapter III The Stress Tensor


1. Forces and Torques. The Laws of Dynamics. Body Forces and Contact Forces


2. Reactions Upon Containers and Submerged Obstacles


3. The Traction Field. Cauchy's Postulate and the Hame

Details

No. of pages:
304
Language:
English
Copyright:
© Academic Press 1977
Published:
Imprint:
Academic Press
eBook ISBN:
9781483220482

About the Author

C. Truesdell

About the Editor

Samuel Eilenberg

Affiliations and Expertise

Columbia University

Hyman Bass

Affiliations and Expertise

Department of Mathematics, Columbia University, New York, New York

Ratings and Reviews