Principles of Engineering Mechanics: Kinematics — The Geometry of MotionSpringer Science & Business Media, 1986 M01 31 - 402 páginas Separation of the elements of classical mechanics into kinematics and dynamics is an uncommon tutorial approach, but the author uses it to advantage in this two-volume set. Students gain a mastery of kinematics first – a solid foundation for the later study of the free-body formulation of the dynamics problem. A key objective of these volumes, which present a vector treatment of the principles of mechanics, is to help the student gain confidence in transforming problems into appropriate mathematical language that may be manipulated to give useful physical conclusions or specific numerical results. In the first volume, the elements of vector calculus and the matrix algebra are reviewed in appendices. Unusual mathematical topics, such as singularity functions and some elements of tensor analysis, are introduced within the text. A logical and systematic building of well-known kinematic concepts, theorems, and formulas, illustrated by examples and problems, is presented offering insights into both fundamentals and applications. Problems amplify the material and pave the way for advanced study of topics in mechanical design analysis, advanced kinematics of mechanisms and analytical dynamics, mechanical vibrations and controls, and continuum mechanics of solids and fluids. Volume I of Principles of Engineering Mechanics provides the basis for a stimulating and rewarding one-term course for advanced undergraduate and first-year graduate students specializing in mechanics, engineering science, engineering physics, applied mathematics, materials science, and mechanical, aerospace, and civil engineering. Professionals working in related fields of applied mathematics will find it a practical review and a quick reference for questions involving basic kinematics. |
Contenido
Kinematics of a Particle | 3 |
12 Primitive Terms | 4 |
13 Motion and Particle Path | 6 |
14 Velocity and Acceleration | 9 |
15 Some Basic Classifications of Problems | 15 |
16 Uniform Motion | 22 |
17 Velocity and Acceleration Referred to an Intrinsic Frame | 26 |
18 Summary of Particle Kinematics | 40 |
310 The Parallel Axis Theorem | 194 |
311 Chasles Screw Displacement Theorem | 197 |
312 Composition of Finite Rotations | 202 |
References | 214 |
Problems | 215 |
Motion Referred to a Moving Reference Frame and Relative Motion | 229 |
42 An Introductory Example | 231 |
43 Derivative of a Vector Referred to a Moving Reference Frame | 232 |
19 Special Topics | 42 |
References | 65 |
Kinematics of Rigid Body Motion | 85 |
22 Displacements of a Rigid Body | 86 |
23 Rotation about a Fixed Line | 87 |
24 The Imbedded Reference Frame | 91 |
25 The General Displacement of a Rigid Body | 92 |
26 Infinitesimal Displacement of a Rigid Body | 94 |
27 Composition of Infinitesimal Rotations | 95 |
28 Velocity and Acceleration of Points of a Rigid Body | 98 |
29 Some Applications of the Basic Equations | 102 |
210 A Basic Invariant Property of the Angular Velocity Vector | 123 |
211 Chasles Theorem on Screw Motions | 126 |
References | 128 |
Problems | 129 |
Finite Rigid Body Displacements | 151 |
32 Index Notation | 152 |
33 Introduction to Tensors | 155 |
34 The Rotator | 168 |
35 The Rotation Tensor | 173 |
36 Change of Basis and Transformation Laws | 175 |
37 Rotation about a Fixed Point | 183 |
38 Eulers Theorem | 186 |
39 Fundamental Invariant Property of the Rotator | 192 |
44 Kinematic Chain Rule for Angular Velocity Vectors | 240 |
45 The Composition Rule for Several Angular Accelerations | 251 |
46 Velocity and Acceleration Referred to a Moving Frame | 260 |
47 Simple Relative Motion | 264 |
48 Velocity and Acceleration in Special Curvilinear Coordinates | 267 |
49 More Examples of Motion Referred to a Moving Frame | 282 |
410 Motion Referred to an Earth Frame | 295 |
411 Summary of the Principal Equations | 303 |
412 Some Special Advanced Topics | 304 |
References | 318 |
The Elements of Vector Calculus | 353 |
A2 Derivative of a Vector Function of a Scalar Variable | 357 |
A3 Integration of a Vector Function of a Scalar Variable | 362 |
Problems | 364 |
The Elements of Matrix Algebra | 365 |
B2 The Elementary Operations | 366 |
B3 Determinant of a Matrix | 371 |
B4 The Inverse of a Matrix | 374 |
377 | |
Problems | 378 |
Answers to Selected Problems | 381 |
387 | |
Otras ediciones - Ver todas
Principles of Engineering Mechanics: Volume 1: Kinematics Millard F. Beatty Sin vista previa disponible - 1986 |