Mechanics (eBook)

B. Skalmierski (Autor)

eBook Download: PDF

2013 | 1. Auflage
454 Seiten
Elsevier Science (Verlag)
978-1-4832-9164-2 (ISBN)

Infos

Since mechanics is the science of motion, studies in this field now cover a wider range of problems than has been the case in earlier classical approaches. This has been achieved by the inclusion of aspects relating to the mechanics of continuous media, or strength problems. The topics covered in this book present a comprehensive treatment of the subject providing a broader perspective to the meaning of mechanics, in the modern sense of the word.Problems in the areas of strength of materials, hydromechanics and theory of elasticity are examined. The author has also endeavoured to show a certain universality of some methods seemingly specific to mechanics by tackling some problems involving electrical or electromechanical systems but based on Lagrange's equations.The book has been designed to emphasize that mechanics is a deductive system, where the aim is not only to present mechanics as the science of motion but also to show that it serves as a bridge between mathematics and its applications, in the broadest sense of the word. Mechanical problems have inspired great mathematicians to come to grips with new mathematical problems, an excellent example here being the problem of the brachistochrone which initiated the development of the variational calculus. The book gives a comprehensive overview on new theoretical findings, and gives many applications which will prove indispensable to all those interested in mechanical and allied problems.

Inhalt

Front Cover 
1 
Mechanics 4
Copyright Page 5
Table of Contents 8
Preface 6
Introduction 12
1. Vectors 16
2. Tensors 27
Chapter 1. Kinematics of a Particle 37
3. Motion of a particle. Trajectories 37
4. The velocity concept 40
5. Acceleration 42
6. Motion of a particle in curvilinear coordinates 49
Chapter 2. Kinematics of a Body 64
7. Analysis of the motion of a continuous medium 64
8. The general motion of a rigid body 72
9. Relative motion 88
10. Plane motion of a rigid body 100
11. Examples of the determination of velocities and accelerations in the motion of plane mechanisms 108
Chapter 3. Particle Dynamics 134
12. Fundamental definitions and theorems 134
13. Rectilinear motion of a particle 137
14. Curvilinear motion of a particle 143
15. Centre of mass and centre of gravity of a particle system 147
16. Law of variation of momentum 153
17. Law of variation of angular momentum 159
Chapter 4. Fundamentals of the Dynamics of Continuous Media 163
18. Preliminary concepts 163
19. Body and surface tension 172
20. The law of variation of momentum for a continuous medium 179
21. The law of variation of angular momentum for a continuous medium 183
22. Work and energy in continuous systems 184
23. Comments and addenda 187
Chapter 5. Dynamics of Rigid Bodies 192
24. Moments of inertia of rigid bodies 192
25. The angular momentum of a rigid body in general motion 198
26. Angular momentum in circular motion 199
27. Euler's equations 201
28. The kinetic energy of rigid bodies in general motion 207
Chapter 6. Dynamics in Relative Motion 213
29. Differential equation of the motion of a particle in a non-inertial system 213
30. The dynamics of rigid bodies in relative motion 215
Chapter 7. Statics and Dynamics of Some Solids and Liquids 220
31. Preliminary discussion 220
32. The elastic body 220
33. Clapeyron's systems 237
34. Viscoelastic bodies 251
35. Pascal's liquid 259
36. Viscous liquids 266
Chapter 8. Fundamentals of Analytical Mechanics 274
37. Generalized coordinates and degrees of freedom of a mechanical system 274
38. D'Alembert's and Hamilton's principles 281
39. Lagrange equation of the first kind 286
40. Lagrange equation of the second kind 290
41. The problem of motion of mechanisms 297
42. Kinetic energy of a system 307
43. Impulsive motion 308
44. Gyroscopic and dissipative forces 312
45. The Lagrange equations for electromechanical systems 315
46. Hamilton's canonical equations 318
47. The total energy of a mechanical system 320
48. Configurational space 321
49. The stability of mechanical systems 324
Chapter 9. Vibrations of Systems with One Degree of Freedom 340
50. Preliminary discussion 340
51. Free vibrations of harmonic oscillators 343
52. The influence of dissipative forces on the free vibration of harmonic oscillators 352
53. Forced vibrations of harmonic oscillators 356
54. Vibrations of harmonic oscillators with kinematical input 364
55. Vibrations of harmonic oscillators under periodic input (exciting) forces 366
56. Vibrations of non-linear systems 369
Chapter 10. Vibrations of Systems with Many Degrees of Freedom 384
57. Preliminary discussion 384
58. Problems of linearization of the equations 385
59. Free vibrations of conservative systems 389
60. Normal coordinates 398
61. Forced vibrations of a system 399
62. Free vibrations of dissipative systems 400
63. Forced vibrations in dissipative systems 402
64. Vibrations of Clapeyron's system 403
Chapter 11. Vibrations of Systems with an Infinite Number of Degrees of Freedom 406
65. Preliminary discussion 406
66. Solution of a one-dimensional problem 407
67. Forced vibrations of a continuous system 416
68. Differential equations of vibration for some continuous elastic media 418
69. Approximate solution methods 433
Bibliography 444
Subject index 450

Produkt-Details

• Erscheint lt. Verlag: 22.10.2013
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 1-4832-9164-2 / 1483291642
• ISBN-13: 978-1-4832-9164-2 / 9781483291642