The Rational Mechanics of Flexible or Elastic Bodies 1638–1788

Content: 
Front Matter....Pages 1-14
Remarks of the ancients on vibration and elasticity....Pages 15-18
Western researches before 1600....Pages 18-23
The vibrating string, the breaking of a beam, and the catenary in Galileo’s Discorsi (1638)....Pages 24-28
The unpublished work of Huygens on the suspension bridge (1646), the breaking of a beam (1662), the vibrating string (1673), and the vibrating rod (1688)....Pages 28-33
The contest to find the catenary (1690)....Pages 34-44
Researches on theoretical and experimental elasticity by James Riccati (1720–1723) and others....Pages 44-50
Experiments on the nodes of vibrating bodies by Noble and Pigot (1674), Sauveur (1696–1701), de la Hire (1709), and Zendrini (1715–1716)....Pages 50-53
Summary: Euler’s heritage....Pages 53-58
Further researches on the elastica; Euler’s general solution for linear vibration problems (1735–1739)....Pages 59-64
The first differential equations of motion: John Bernoulli’s and d’Alembert’s treatments of the hanging cord (1742–1743)....Pages 64-75
Summary to 1748....Pages 75-88
Miscellaneous polemics (1760–1767)....Pages 88-96
Miscellaneous polemics to 1788....Pages 96-109
Summary of the theory of the vibrating string to 1788....Pages 109-114
The earliest researches on non-uniform strings: Simple modes for special cases, and Euler’s general inverse method (1752–1765)....Pages 114-117
Polemics, errors, and further special cases (1770–1788)....Pages 118-129
Plane vibrations of a heavy cord hung from one end....Pages 129-132
Discrete models....Pages 132-136
The distinction of different kinds of buckling by Daniel & John III Bernoulli (1766)....Pages 136-141
Miscellaneous researches (1754–1768)....Pages 142-146
An evaluation from the eighteenth century: Lagrange’s Méchanique Analitique (1788)....Pages 146-150
Some later evaluations: Chladni (1802), T. Young (1807), Love (1892)....Pages 150-153
A modern evaluation....Pages 154-165
Back Matter....Pages 165-170
....Pages 170-178