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.

Contenu

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
Couples
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
Appendix
Index