Analytical Elements of Mechanics (eBook)

Front Cover 1
Analytical Elements of Mechanics 4
Copyright Page 5
Table of Contents 12
ACKNOWLEDGMENT 6
PREFACE 8
Chapter 1. VECTOR ALGEBRA 18
1.1 Terminology 18
1.2 Notation 19
1.3 Equality 20
1.4 The product of a vector v and a scalar s: sv or vs 20
1.5 Zero vectors 21
1.6 The quotient of a vector v and a scalar s: v/s or v/s 22
1.7 Unit vectors 22
1.8 The sum of a vector v1 and a vector v2: v1 + v2 or v2 + v1 24
1.9 The sum of n vectors vif i = 1, 2 . . . , n: Sn i=1 vi or V1 + V2 + . . . + Vn 26
1.10 Resolution of a vector v into n components 29
1.11 Methods for resolving a vector into three mutually perpendicular components 33
1.12 Resolutes of a vector v 37
1.13 The angle between a vector a and a vector b: (a, b) or (b, a) 38
1.14 The scalar (dot) product of a vector a and a vector b: a · b or b · a 39
1.15 The vector (cross) product of a vector a and a vector b: a X b 48
1.16 The scalar triple product of three vectors a, b, c: [a,b, c] 53
1.17 The vector triple product of three vectors a, b, c: a X (bXc) 55
Chapter 2. CENTROIDS AND MASS CENTERS 58
2.1 The position vector of one point relative to another 58
2.2 The relationship between the position vector p and the coordinates x, y, z, of a point P 59
2.3 The first moment of a point P with respect to a point O 61
2.4 The centroid of a set of points 61
2.5 The centroid of a curve, surface, or solid 70
2.6 The mass center of a set of particles 87
2.7 The mass center of a continuous body 87
Chapter 3. MOMENTS AND COUPLES 98
3.1 The moment of a bound vector about a point 98
3.2 The moment of a bound vector about a line 99
3.3 Moments of a system of bound vectors 108
3.4 Definition 114
3.5 Definition 121
3.6 Definition 136
Chapter 4. STATIC EQUILIBRIUM 144
4.1 Force 144
4.2 Mutual gravitational attraction of particles 144
4.3 Mutual gravitational attraction of a particle and a continuous body 150
4.4 Mutual gravitational attraction of two continuous bodies 156
4.5 Force systems associated with contact surfaces 161
4.6 Equilibrium equations 162
4.7 The relationship between reactions across a given surface 167
4.8 Contact forces and physical properties 169
4.9 Several-body problems 181
4.10 Traction 187
4.11 Friction 197
PROBLEM SETS 208
PROBLEM SET 1 210
PROBLEM SET 2 211
PROBLEM SET 3 212
PROBLEM SET 4 214
PROBLEM SET 5 218
PROBLEM SET 6 221
PROBLEM SET 7 223
PROBLEM SET 8 226
PROBLEM SET 9 229
PROBLEM SET 10 232
PROBLEM SET 11 234
PROBLEM SET 12 235
PROBLEM SET 13 239
PROBLEM SET 14 242
PROBLEM SET 15 245
PROBLEM SET 16 253
INDEX 264