Analytical Elements of Mechanics - 1st Edition - ISBN: 9781483231280, 9781483274201

Analytical Elements of Mechanics

1st Edition

Authors: Thomas R. Kane
eBook ISBN: 9781483274201
Imprint: Academic Press
Published Date: 1st January 1959
Page Count: 266
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Analytical Elements of Mechanics, Volume 1, is the first of two volumes intended for use in courses in classical mechanics. The books aim to provide students and teachers with a text consistent in content and format with the author’s ideas regarding the subject matter and teaching of mechanics, and to disseminate these ideas.
The book opens with a detailed exposition of vector algebra, and no prior knowledge of this subject is required. This is followed by a chapter on the topic of mass centers, which is presented as a logical extension of concepts introduced in connection with centroids. A theory of moments and couples is constructed without reference to forces, these being mentioned only in illustrative examples. This is done because it eventually becomes necessary to apply the theory to systems of vectors which are not forces, such as momenta and impulses. Equilibrium is discussed in the final chapter, preceded by extended examination of the concept of force.

Table of Contents

1 Vector Algebra

1.1 Terminology

1.2 Notation

1.3 Equality

1.4 the Product of a Vector and a Scalar

1.5 Zero Vectors

1.6 The Quotient of a Vector and a Scalar

1.7 Unit Vectors

Vector Addition

1.8 Sum of Two Vectors

1.9 The Sum of Several Vectors

Components of a Vector

1.10 Resolution into Components

1.11 Methods for Resolution

1.12 Resolutes

Scalar Multiplication of Vectors

1.13 Angle between Two Vectors

1.14 Scalar Product of Two Vectors

Vector Multiplication of Vectors

1.15 Vector Product of Two Vectors

Products of Three Vectors

1.16 Scalar Triple Product

1.17 Vector Triple Product

2 Centroids and Mass Centers

2.1 Position Vector

2.2 Position Vector and Coordinates

2.3 First Moment

Sets of Points

2.4 Centroid

Curves, Surfaces, and Solids

2.5 Centroid

Sets of Particles

2.6 Mass Center

Continuous Bodies

2.7 Mass Center

3 Moments and Couples

3.1 Moment about a Point

3.2 Moment about a Line

3.3 System of Bound Vectors


3.4 Definition

Equivalence, Replacement, and Reduction

3.5 Definition

Zero Systems

3.6 Definition

4 Static Equilibrium

4.1 Force

Gravitational Forces

4.2 Particles

4.3 Particle and Body

4.4 Two Bodies

Contact Forces

4.5 Contact Surfaces

4.6 Equilibrium Equations

4.7 Reactions across One Surface

4.8 Physical Properties

4.9 Several-Body Problems

4.10 Traction

4.11 Friction

Problem Sets

Problem Set 1

Problem Set 2

Problem Set 3

Problem Set 4

Problem Set 5

Problem Set 6

Problem Set 7

Problem Set 8

Problem Set 9

Problem Set 10

Problem Set 11

Problem Set 12

Problem Set 13

Problem Set 14

Problem Set 15

Problem Set 16




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© Academic Press 1959
Academic Press
eBook ISBN:

About the Author

Thomas R. Kane

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