Essays in the History of Mechanics

Title page......Page 1
Foreword......Page 5
Contents......Page 7
1. Proem......Page 11
2. Leonardo and Early Engineering......Page 13
3. Did Leonardo Experiment?......Page 17
4. Leonardo on Beams......Page 23
5. Leonardo\'s Method of Inquiry, I......Page 30
6. Leonardo on Force and Motion......Page 31
7. Birth of the History of Mechanics......Page 35
8. Mediaeval Kinematics and Dynamics......Page 40
9. Leonardo and the Tradition......Page 43
10. Uniformly Accelerated Motion in the Void and on the Inclined Plane......Page 44
11. Leonardo\'s Method of Inquiry, II......Page 49
12. Science and Art......Page 51
13. Leonardo as a Mathematician......Page 52
14. Perspective and Motion in Leonardo\'s Painting......Page 63
15. Leonardo on General Aspects of Fluid Motion......Page 72
16. Leonardo on Waves and Vortices......Page 79
17. Leonardo\'s Principles of Continuity and Circulation......Page 86
18. Leonardo\'s Fame......Page 89
Acknowledgment......Page 92
II. A Program toward Rediscovering the Rational Mechanics of the Age of Reason......Page 95
1. Newton\'s Principia (1687)......Page 98
2. Scientific Methods and Scenes in the Age of Reason......Page 103
3. The Discoveries of James Bernoulli......Page 111
4. Early Efforts to Clarify, Extend, and Organize the Principles of Mechanics......Page 115
5. The Proper Frequencies and Simple Modes of Vibrating Systems before the Discovery of Equations of Motion......Page 117
6. Fluid Mechanics before the Discovery of Differential Equations of Equilibrium and Motion......Page 120
7. The Earliest Differential Equations of Motion for Systems......Page 122
8. Definitive Formulation of the Principle of Linear Momentum: Euler\'s \"First Principles of Mechanics\" (\"Newton\'s Equations \") (1750)......Page 124
9. Rigid Bodies, and the Distinction of Mass from Inertia......Page 127
10. Problems of Vibration and Wave Motion seen from the Equations of Motion......Page 128
11. The Concept of Normal Stress, and the Principles of Hydrodynamics......Page 131
12. The Laws of Elasticity, and the Concept of Shear Stress......Page 134
13. The Principle of Moment of Momentum......Page 138
14. The Invariance of the Laws of Mechanics, and Lagrange\'s Mechanique Analitique (1788)......Page 141
15. Retrospect: Experience, Theory, and Experiment in the Age of Reason......Page 145
References......Page 146
1. Newton\'s Principia, Book I......Page 148
2. Newton\'s Principia, Book II......Page 154
3. Success and Tradition in Mechanics before Newton......Page 159
4. Some of the Bernoullis\' Work......Page 166
5. Rigid Motion, Moment of Momentum, the Elastica, and Euler\'s Laws of Mechanics......Page 172
6. The Mechanique Analitique of Lagrange, and Later Reactions......Page 183
7. Nineteenth-Century Misconceptions of Newton\'s Work and Program. The Position of Faraday......Page 185
8. Our Legacy from Newton......Page 192
Bibliographical Note......Page 193
IV. The Creation and Unfolding of the Concept of Stress......Page 194
1. Cauchy\'s Laws of Motion (1822)......Page 196
2. Subject of this Lecture......Page 201
3. The Central Role of Euler\'s Hydrodynamics (1750-1755). What it Achieved, and what it Obscured......Page 202
4. Stevin\'s Principle of Solidification (1586)......Page 204
5. Galileo\'s Rupture Stress (1638)......Page 210
6. Pardies\' and James Bernoulli\'s Concept of Tension in a Flexible Line (1673, 1691-1704)......Page 214
7. Leibniz, James Bernoulli, and Parent on the Variation of Tension in the Fibres of a Loaded Beam (1684, 1691, 1713)......Page 216
8. Mathematical Generalizations of Archimedes\' and Stevin\'s Hydrostatics before the General Equations (1687-1749)......Page 221
9. Influences of Constitutive Properties on the General Concept of Stress in the Work of James Bernoulli and Euler on the Bending of Bars (1705, 1727, 1779)......Page 225
10. The Hydraulics of Daniel Bernoulli, John Bernoulli, and Euler (1730-1752)......Page 229
11. The first Attempts at Hydrodynamics by Euler and D\'Alembert (1745-1749)......Page 235
12. Euler\'s Hydrodynamics (1750-1766)......Page 240
13. Resultant Shear Force, and Euler\'s General Theory of Deformable Lines (1771-1774)......Page 242
15. A Final Remark about Cauchy......Page 246
Bibliographical Note......Page 248
1. The Standard Law of Moment of Momentum for Physicists......Page 249
2. The Two Concepts of the Law of Moment of Momentum......Page 253
3. Newton, Huygens, and Lagrange Published Nothing on the Two Concepts......Page 254
4. The Fundamental Work of James Bernoulli on the Center of Oscillation (1686-1703)......Page 258
5. Daniel Bernoulli and Euler on the Dependence or Independence of the Law of Moment of Momentum in 1744......Page 262
6. Euler\'s General Principle of Linear Momentum (1750) and Discovery of the Equations of Motion of a Rigid Body......Page 267
7. Euler\'s Fundamental Laws of Mechanics (1775)......Page 269
8. Transition to the Newtonians (1833 onward)......Page 273
Appendix: Recent Views on the Principles of Mechanics......Page 278
Bibliographical Note......Page 281
1. The Eighteenth Century......Page 282
2. Herapath (1816-1821)......Page 293
3. Joule and Kronig (1851, 1856)......Page 299
4. Waterston (1843-1846)......Page 302
5. In Praise of Disorganization of Science......Page 309
Bibliographical Note......Page 313
VII. Reactions of the History of Mechanics upon Modern Research......Page 315
1. Proem......Page 316
2. The Elastica of Optimum Section......Page 319
3. The Elastica of Desired Shape when Loaded......Page 320
4. Methods of Approach to General Questions......Page 325
5. The Axioms of Forces......Page 331
6. Seventeenth-Century Parallels to the Obscurity of Thermodynamics and Thermostatics......Page 334
Acknowledgment......Page 341
References......Page 342
Bibliographical Note......Page 343
1. What is Rational Mechanics?......Page 344
2. A Classical Example: The Vorticity Theorems of Helmholtz, Kelvin, and Ertel......Page 350
3. Reissner\'s Variational Principle in Linear Elasticity......Page 355
4. \"St. Venant\'s Principle\" according to v. Mises and Sternberg......Page 356
5. Large Elastic Deformations......Page 359
6. Non-linear Viscosity, and Non-linear Theories in General......Page 362
7. Experiment and Theory......Page 367
9. Rate Theories of Material Behavior......Page 368
10. Khinchin\'s Ergodic Theorem......Page 370
12. Apology......Page 374
Bibliographical Note......Page 376
Index of Names......Page 377
Index of Subjects......Page 387