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The Evolution of Dynamics: Vibration Theory from 1687 to 1742 Vibration Theory from 1687 to 1742

In 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. The relationship that existed between these subject!! is obscured in retrospection for it is now almost impossible not to view (linear) V...

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Bibliographic Details
Main Authors: Cannon, J. T., Dostrovsky, S. (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 1981, 1981
Edition:1st ed. 1981
Series:Studies in the History of Mathematics and Physical Sciences
Subjects:
Mathematical Physics
Mathematics
Theoretical, Mathematical And Computational Physics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1. 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

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