1 We search the concepts and methods ) of the theory of deformable sonds from GALILEO to LAGRANGE. Neither of them achieved much in our subject, but their works serve as 2 termini: With GALILEO's Discorsi in 1638 our matter begins ) (for this is the history of mathematical theory), while LAGRANGE's Mechanique Analitique closed the mechanics of 1) There are three major historical works that bear on our subject. The first is A history of the theory of elasticity and of the strength of materials by I. ToDHUNTER, "edited and completed" by K. PEARSON, Vol. I, Cambridge, 1886. Unfortunately it is necessary to give warning that this book fails to meet the standard set by the histories ToDHUNTER lived to finish. Much of what ToDHUNTER left seems to be rather the rough notes for a book than the book itself; the parts due to PEARSON are fortunately distinguished by square brackets. Researches prior to 1800 are disposed of in the first chapter, 79 pages long and almost entirely the work of PEARSON; as frontispiece to a work whose title restricts it to theory he saw fit to supply a possibly original pen drawing entitled "Rupture. Sur faces of Cast-Iron".
Erscheinungsdatum: 01.01.1960

lgrsnf/Truesdell C. The rational mechanics of flexible or elastic bodies 1638-1788.. Introduction to Vol. X, XI of Opera Omnia by L.Euler (Birkhauser, 1960)(ISBN 3764314419)(400dpi)(T)(O)(435s)_MW_.djvu

The rational mechanics of flexible or elastic bodies : 1638-1788 : introduction to Leonhardi Euleri Opera Omnia / vol. 10. et 11., seriei secundae

The rational mechanics of flexible or elastic bodies : 1638-1788 : introduction to Leonhardi Euleri opera omnia vol. X et XI, seriei secundae

The rational mechanics of flexible or elastic bodies 1638 - 1788: Introduction to Vol. X and XI (Leonhard Euler, Opera Omnia) (Vol 11/2)

The rational mechanics of flexible or elastic bodies 1638 - 1788. 2nd part/2nd section: Introduction to Vol. X and XI

Clifford Ambrose Truesdell

Euler, Leonhard

Auctoritate et impensis Societatis scientiarum naturalium Helveticae

Springer Basel

Birkhauser

Leonhardi Euleri opera omnia, Turici, 1960

1 edition, January 1, 1980

1960, 1980-01-01

Germany, Germany

Cover
Title page
CONTENTS
Foreword
Prefatory Note concerning the presumed technological origin of the science of elasticity
PROLOGUE
1. Remarks of the ancients on vibration and elasticity
2. Western researches before 1600
3. BEECKMAN on the suspension bridge (1614-1615), on vibration (1614-1618), and on elasticity (1620-1630)
4. MERSENNX on vibration and rupture (1623-1636)
PART I. THE EARLIEST SPECIAL PROBLEMS, 1638-1730
5. The vibrating string, the breaking of a beam, and the catenary in GALILEO'S Discorsi (1638)
6. The unpublished work of HUYGENS on the suspension bridge (I646), the breaking of a beam (1662), the vibrating string (1673), and the vibrating rod (1688)
7. PARDIES' essays on the catenary and on elastic beams (1673)
8. HOOKE'S law of spring (1675, 1678) and researches on the arch (1675), on ropes (1669), and on sound (1675-1681)
9. MARIOTTE and LEIBNIZ on elastic beams (1684)
10. The contest to find the catenary (1690)
11. JAMES BERNOULLI'S researches on the general theory of flexible lines (I691-1704), and later work to 1717
12. JAMES BERNOULLI'S first researches on the elastica (1691-1694)
13. JAMES BERNOULLI'S attempts toward a theory of the neutral fibre (1695-1705)
14. PARENT'S researches on the neutral fibre (1704-1713)
15. Researches on theoretical and experimental elasticity by JAMES RICCATI (1720-1723) and others
16. Experiments on the nodes of vibrating bodies by NOBLE and PIGOT (c. 1674), SAUVEUR (1696-1701), DE LA HIRE (1709), and ZENDRINI (1715-1716)
17. TAYLOR'S analysis of the continuous vibrating string (1713)
18. JOHN BERNOULLI'S analysis of the loaded vibrating string (1727)
19. Summary: EULER'S heritage
PART II. THE BEGINNINGS OF THE GENERAL THEORIES, 1727-1748
20. EULER'S derivation of JAMES BERNOULLI'S law of bending from HOOKE'S law of extension; introduction of the modulus of extension (1727)
21. EULER'S unification of the catenary and the elastica (1728)
22. MUSSCHENBROEK'S experimental discovery of the law of buckling in compression (1729)
23. DANIEL BERNOULLI'S discovery of the simple modes and proper frequencies of vibrating systems (1733), and related work of EULER
24. DANIEL BERNOULLI'S and EULER'S first calculations of simple modes and proper frequencies for the transverse oscillations of bars (1734-1735)
25. Further researches on the elastica; EULER'S general solution for linear vibration problems (1735-1739)
26. The first differential equations of motion: JOHN BERNOULLI'S and D'ALEMBERT'S treatments of the hanging cord (1742-1743)
27. DANIEL BERNOULLI'S definitive work on the transverse vibrations of bars (1740-1742)
28. EULER'S treatise on elastic curves (1743). 1. Static deflection
29. EULER'S treatise on elastic curves (1743). II. Vibrations
30. EULER'S equations of finite motion for linked systems and for the continuous string (1744)
31. EULER'S general solution for longitudinal vibration of the loaded elastic cord ( 1748)
32. Summary to 1748
PART III. THE CONTROVERSY OVER SMALL PLANE VIBRATIONS OF A STRING OF UNIFORM THICKNESS, 1746-1788
33. D'ALEMBERT'S first memoir (1746): The partial differential equation and its solution by an "equation"
34. EULER'S first memoir (1748): The solution by arbitrary functions
35. EULER'S "first principles of mechanics" (1750)
36. DANIEL BERNOTILLI'S memoirs on the composition of simple modes (1753)
37. EULER'S second memoir (1754): The central importance of the partial differential equation
38. LAGRANGE'S first memoir (1759): The explicit solution for the loaded string, and a faulty passage to the limit
39. Miscellaneous polemics (1760-1767)
40. EULER'S researches on the propagation and reflection of waves (1764-1765)
41. Miscellaneous polemics to 1788
42. Summary of the theory of the vibrating string to 1788
PART IV. RESEARCHES SUBSEQUENT TO EULER'S "FIRST PRINCIPLES OF MECHANICS" (1752-1788)
IV A. The non-uniform vibrating string
43. The earliest researches on non-uniform strings: Simple modes for special cases, and EULER'S general inverse method (1752-1765)
44. Polemics, errors, and further special cases (1770-1788)
IVB. Plane vibrations of a heavy cord hung from one end
45. Plane vibrations of a heavy cord hung from one end
IVC. Plane vibrations of straight or curved rods
46. EULER'S faulty theories of curved rods (1760, 1774)
47. EULER'S definitive work on the ix kinds of transverse vibration of straight rods (1772-1774), and its experimental verification by JORDAN RICCATI (1782) and by CHLADNI (1787)
IVD. Vibrations of membranes and plates
48. EULER'S theory of the vibrating membrane (1759)
49. CHLADNI'S experiments on the vibrations of free plates (1787)
IVE. Discrete models
50. Discrete models
IVF. Plane static deflection and buckling of straight bars
51. EULER'S calculation of buckling loads for columns of non-uniform cross-section (1757)
52. The distinction of different kinds of buckling by DANIEL & JOHN III BERNOULLI (1766)
53. LAGRANGE'S two memoirs (1770, 1773)
54. EULER'S determination of the height at which a heavy vertical column buckles (1776, 1778)
IVG. The statics and dYnamics of skew curves
55. LAGRANGE'S variational equations of motion for flexible lines (1761)
56. EULER'S theory of the skew elastica (1774-1775)
IVH. The laws of elasticity and flexibility
57. Miscellaneous researches (1754-1768)
58. EULER'S introduction of shear force and derivation of the general equations of equilibrium for a deformable line (1771, 1774)
59. COULOMB'S introduction of interior shearing stress (1773)
60. EULER'S formal definition of the modulus of extension and final scaling laws for the frequencies and buckling loads of straight rods (1774, 1776)
61. COULOMB'S experiments on torsion (1777, 1784)
PART V. EVALUATION
62. An evaluation from the eighteenth century: LAGRANGE'S Mechanique Analitique (1788)
63. Some later evaluations: CHLADNI (1802), T. YOUNG (1807), LOVE (1892)
64. A modern evaluation
INDEX OF NAMES

2024-08-04