Skalmierski Mechanics

1. Auflage 2013
ISBN: 978-1-4832-9164-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 27, 454 Seiten, Web PDF

Reihe: Studies in Applied Mechanics

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.

Autoren/Hrsg.

Skalmierski, B.

Inhaltsverzeichnis

1;Front Cover
;1
2;Mechanics;4
3;Copyright Page;5
4;Table of Contents;8
5;Preface;6
6;Introduction;12
6.1;1. Vectors;16
6.2;2. Tensors;27
7;Chapter 1. Kinematics of a Particle;37
7.1;3. Motion of a particle. Trajectories;37
7.2;4. The velocity concept;40
7.3;5. Acceleration;42
7.4;6. Motion of a particle in curvilinear coordinates;49
8;Chapter 2. Kinematics of a Body;64
8.1;7. Analysis of the motion of a continuous medium;64
8.2;8. The general motion of a rigid body;72
8.3;9. Relative motion;88
8.4;10. Plane motion of a rigid body;100
8.5;11. Examples of the determination of velocities and accelerations in the motion of plane mechanisms;108
9;Chapter 3. Particle Dynamics;134
9.1;12. Fundamental definitions and theorems;134
9.2;13. Rectilinear motion of a particle;137
9.3;14. Curvilinear motion of a particle;143
9.4;15. Centre of mass and centre of gravity of a particle system;147
9.5;16. Law of variation of momentum;153
9.6;17. Law of variation of angular momentum;159
10;Chapter 4. Fundamentals of the Dynamics of Continuous Media;163
10.1;18. Preliminary concepts;163
10.2;19. Body and surface tension;172
10.3;20. The law of variation of momentum for a continuous medium;179
10.4;21. The law of variation of angular momentum for a continuous medium;183
10.5;22. Work and energy in continuous systems;184
10.6;23. Comments and addenda;187
11;Chapter 5. Dynamics of Rigid Bodies;192
11.1;24. Moments of inertia of rigid bodies;192
11.2;25. The angular momentum of a rigid body in general motion;198
11.3;26. Angular momentum in circular motion;199
11.4;27. Euler's equations;201
11.5;28. The kinetic energy of rigid bodies in general motion;207
12;Chapter 6. Dynamics in Relative Motion;213
12.1;29. Differential equation of the motion of a particle in a non-inertial system;213
12.2;30. The dynamics of rigid bodies in relative motion;215
13;Chapter 7. Statics and Dynamics of Some Solids and Liquids;220
13.1;31. Preliminary discussion;220
13.2;32. The elastic body;220
13.3;33. Clapeyron's systems;237
13.4;34. Viscoelastic bodies;251
13.5;35. Pascal's liquid;259
13.6;36. Viscous liquids;266
14;Chapter 8. Fundamentals of Analytical Mechanics;274
14.1;37. Generalized coordinates and degrees of freedom of a mechanical system;274
14.2;38. D'Alembert's and Hamilton's principles;281
14.3;39. Lagrange equation of the first kind;286
14.4;40. Lagrange equation of the second kind;290
14.5;41. The problem of motion of mechanisms;297
14.6;42. Kinetic energy of a system;307
14.7;43. Impulsive motion;308
14.8;44. Gyroscopic and dissipative forces;312
14.9;45. The Lagrange equations for electromechanical systems;315
14.10;46. Hamilton's canonical equations;318
14.11;47. The total energy of a mechanical system;320
14.12;48. Configurational space;321
14.13;49. The stability of mechanical systems;324
15;Chapter 9. Vibrations of Systems with One Degree of Freedom;340
15.1;50. Preliminary discussion;340
15.2;51. Free vibrations of harmonic oscillators;343
15.3;52. The influence of dissipative forces on the free vibration of harmonic oscillators;352
15.4;53. Forced vibrations of harmonic oscillators;356
15.5;54. Vibrations of harmonic oscillators with kinematical input;364
15.6;55. Vibrations of harmonic oscillators under periodic input (exciting) forces;366
15.7;56. Vibrations of non-linear systems;369
16;Chapter 10. Vibrations of Systems with Many Degrees of Freedom;384
16.1;57. Preliminary discussion;384
16.2;58. Problems of linearization of the equations;385
16.3;59. Free vibrations of conservative systems;389
16.4;60. Normal coordinates;398
16.5;61. Forced vibrations of a system;399
16.6;62. Free vibrations of dissipative systems;400
16.7;63. Forced vibrations in dissipative systems;402
16.8;64. Vibrations of Clapeyron's system;403
17;Chapter 11. Vibrations of Systems with an Infinite Number of Degrees of Freedom;406
17.1;65. Preliminary discussion;406
17.2;66. Solution of a one-dimensional problem;407
17.3;67. Forced vibrations of a continuous system;416
17.4;68. Differential equations of vibration for some continuous elastic media;418
17.5;69. Approximate solution methods;433
18;Bibliography;444
19;Subject index;450