Introduction to and Andy Ruina and Rudra Pratap

Detailed Contents
Front tables
i
Summary of mechanics . . . . . . . . . . . . . . . . . . . i
Some basic definitions . . . . . . . . . . . . . . . . . . . . ii
Brief Contents 1
Detailed Contents 2
Preface 10
General issues about content, level, organization and style, motivation,
how to study and the use of computers.
0.1 To the student (please read) . . . . . . . . . . . . . . . . . . 14
0.2 A note on computation . . . . . . . . . . . . . . . . . . . . . 18
Box: Informal computer commands . . . . . . . . . . . . . 21
Part I: Basics for Mechanics 22
1 What is mechanics 22
Mechanics can predict forces and motions by using the three pillars of the
subject: I. models of physical behavior, II. geometry, and III. the basic
mechanics balance laws. The laws of mechanics are informally summarized
in this introductory chapter. The extreme accuracy of Newtonian
mechanics is emphasized, despite relativity and quantum mechanics supposedly
having ‘overthrown’ seventeenth century physics. Various uses
of the word ‘model’ are described.
1.1 The three pillars . . . . . . . . . . . . . . . . . . . . . . . . 23
1.2 Mechanics is wrong, why study it . . . . . . . . . . . . . . 29
1.3 The heirarchy of models . . . . . . . . . . . . . . . . . . . . 31
2 Vectors 36
The key vectors for statics, namely relative position, force, and moment,
are used to motivate needed vector skills. Notational clarity is emphasized
because correct calculation is impossible without distinguishing
vectors from scalars. Vector addition is motivated by the need to add
forces and relative positions, dot products are motivated as the tool which
reduces vector equations to scalar equations, and cross products are motivated
as the formula which correctly calculates the heuristically motivated
quantities of moment and moment about an axis.
2