Description
Book SynopsisIn this study we are concerned with Vibration Theory and the Problem of Dynamics during the half century that followed the publication of Newton's Principia. In fact, it was through problems posed by Vibration Theory that a general theory of Dynamics was motivated and discovered.
Table of Contents1. Introduction.- 2. Newton (1687).- 2.1. Pressure Wave.- 2.2. Remarks.- 3. Taylor (1713).- 3.1. Vibrating String.- 3.2. Absolute Frequency.- 3.3. Remarks.- 4. Sauveur (1713).- 4.1. Vibrating String.- 4.2. Remarks.- 5. Hermann (1716).- 5.1. Pressure Wave.- 5.2. Vibrating String.- 5.3. Remarks.- 6. Cramer (1722).- 6.1. Sound.- 6.2. Remarks.- 7. Euler (1727).- 7.1. Vibrating Ring.- 7.2. Sound.- 8. Johann Bernoulli (1728).- 8.1. Vibrating String (Continuous and Discrete).- 8.2. Remark on the Energy Method.- 9. Daniel Bernoulli (1733; 1734); Euler (1736) …..- 9.1. Linked Pendulum and Hanging Chain.- 9.2. Laguerre Polynomials and J0.- 9.3. Double and Triple Pendula.- 9.4. Roots of Polynomials.- 9.5. Zeros of J0.- 9.6. Other Boundary Conditions.- 9.7. The Bessel Functions Jv.- 10. Euler (1735).- 10.1. Pendulum Condition.- 10.2. Vibrating Rod.- 10.3. Remarks.- 11. Johann II Bernoulli (1736).- 11.1. Pressure Wave.- 11.2. Remarks.- 12. Daniel Bernoulli (1739; 1740).- 12.1. Floating Body.- 12.2. Remarks.- 12.3. Dangling Rod.- 12.4. Remarks on Superposition.- 13. Daniel Bernoulli (1742).- 13.1. Vibrating Rod.- 13.2. Absolute Frequency and Experiments.- 13.3. Superposition.- 14. Euler (1742).- 14.1. Linked Compound Pendulum.- 14.2. Dangling Rod and Weighted Chain.- 15. Johann Bernoulli (1742) no.- 15.1. One Degree of Freedom.- 15.2. Dangling Rod.- 15.3. Linked Pendulum I.- 15.4. Linked Pendulum II.- Appendix: Daniel Bernoulli’s Papers on the Hanging Chain and the Linked Pendulum.- Theoremata de Oscillationibus Corporum.- De Oscillationibus Filo Flexili Connexorum.- Theorems on the Oscillations of Bodies.- On the Oscillations of Bodies Connected by a Flexible Thread.
