Analytical Elements of Mechanics (eBook)
354 Seiten
Elsevier Science (Verlag)
978-1-4832-7421-8 (ISBN)
The book first offers information on the differentiation of vectors, including vector functions of a scalar variable; derivatives of sums and products; vector tangents of a space curve; vector binormals of a space curve; and Taylor's theorem for vector functions. The manuscript then ponders on kinematics, as well as angular velocity and acceleration, absolute and relative velocity and acceleration, and rates of change of orientation of a rigid body.
The text examines second moments and laws of motion. Discussions focus on second moments of sets of particles and continuous bodies, second moments of a point, motions of rigid bodies, and linear and angular momentum.
The publication is a dependable reference for readers interested in the dynamics of the analytical elements of mechanics.
Analytical Elements of Mechanics, Volume 2: Dynamics focuses on the processes, methodologies, approaches, and technologies involved in classical mechanics. The book first offers information on the differentiation of vectors, including vector functions of a scalar variable; derivatives of sums and products; vector tangents of a space curve; vector binormals of a space curve; and Taylor's theorem for vector functions. The manuscript then ponders on kinematics, as well as angular velocity and acceleration, absolute and relative velocity and acceleration, and rates of change of orientation of a rigid body. The text examines second moments and laws of motion. Discussions focus on second moments of sets of particles and continuous bodies, second moments of a point, motions of rigid bodies, and linear and angular momentum. The publication is a dependable reference for readers interested in the dynamics of the analytical elements of mechanics.
Front Cover 1
Dynamics 4
Copyright Page 5
Table of Contents 10
PREFACE 6
Chapter 1. DIFFERENTIATION OF VECTORS 18
1.1 Vector functions of a scalar variable 18
1.2 The first derivative of a vector function 26
1.3 The second and higher derivatives of vector functions 29
1.4 Derivatives of sums 30
1.5 Derivatives of products 31
1.6 Derivatives of implicit functions 36
1.7 The first derivative of a unit vector which remains perpendicular to a line fixed in a reference frame 37
1.8 Taylor's theorem for vector functions 43
1.9 Vector tangents of a space curve 46
1.10 Vector binormals of a space curve 50
1.11 The vector principal normal of a space curve 55
1.12 The vector radius of curvature of a space curve 56
1.13 The Serret-Frenet formulas 59
Chapter 2. KINEMATICS 66
2.1 Rates of change of orientation of a rigid body 66
2.2 Angular velocity 71
2.3 Angular acceleration 85
2.4 Relative velocity and acceleration 97
2.5 Absolute velocity and acceleration 101
Chapter 3. SECOND MOMENTS 130
3.1 Second moments of a point 130
3.2 Second moments of a set of points 137
3.3 Principal directions, axes, planes, second moments, and radii of gyration of a set of points 143
3.4 Second moments of curves, surfaces, and solids 159
3.5 Second moments of sets of particles and continuous bodies 176
Chapter 4. LAWS OF MOTION 188
4.1 Inertia forces and force systems 188
4.2 D'Alembert's principle 199
4.3 Motions of rigid bodies 224
4.4 Linear and angular momentum 247
PROBLEM SETS 296
PROBLEM SET 1 298
PROBLEM SET 2 300
PROBLEM SET 3 302
PROBLEM SET 4 306
PROBLEM SET 5 310
PROBLEM SET 6 316
PROBLEM SET 7 320
PROBLEM SET 8 324
PROBLEM SET 9 329
PROBLEM SET 10 331
PROBLEM SET 11 336
PROBLEM SET 12 338
APPENDIX: Centroidal Principal Axes and Squares of Centroidal Principal Radii of Gyration of Curves, Surfaces, and Solids 342
CURVES 344
SURFACES 345
SOLIDS 347
INDEX 350
| Erscheint lt. Verlag | 22.10.2013 |
|---|---|
| Sprache | englisch |
| Themenwelt | Naturwissenschaften ► Chemie |
| Naturwissenschaften ► Physik / Astronomie ► Mechanik | |
| Technik | |
| ISBN-10 | 1-4832-7421-7 / 1483274217 |
| ISBN-13 | 978-1-4832-7421-8 / 9781483274218 |
| Haben Sie eine Frage zum Produkt? |
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