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Introduction

Chapter
Part of the History of Mechanism and Machine Science book series (HMMS, volume 12)

Abstract

Perhaps the best known use of pendulums is as the basis of clocks in which a pendulum controls the rate at which the clock runs. Many clocks have visible pendulums. Indeed, the association of pendulums with clocks is so pervasive that, since the advent of quartz clocks, it is possible to buy clocks with visible swinging pendulums that are independent of the timekeeping of the clock. Interest in the behaviour of pendulums, in particular calculation of times of swing, dates back to the observation, usually attributed to Galileo, that the time of swing of a pendulum is independent of the amplitude of its oscillations. In other words the pendulum is isochronous. The story is that in 1581 Galileo was sitting in Pisa Cathedral, and compared the times of oscillations of suspended lamps with the pulse in his wrist. The seminal book on theoretical and practical aspects of pendulums, as applied to clocks, is ‘Horologium’ by Christiaan Huygens published in 1658. For the four centuries following Huygens’ seminal work pendulum behaviour was regarded as essentially regular. The important properties of a pendulum were assumed to be its time of swing, and the variability of the time of swing. Much effort was devoted to theoretical and practical aspects of improving the accuracy of pendulums used to control clocks. Scientific applications of pendulums include the Foucault pendulum used to demonstrate rotation of the Earth, and the Charpy impact test, used to measure the fracture resistance of metals. Industrial applications include the Watt steam governor used to regulate steam engines and the tension leg platforms used for the offshore recovery of oil and gas. Recreational uses include children’s swings, and pendulum harmonographs used to draw figures known as harmonograms. Pendulums are sometimes used for occult purposes. More recently it has been appreciated that pendulum behaviour can be irregular. In other words a pendulum can be a chaotic system. This means that chaos theory is needed for understanding of pendulum behaviour. In scientific terminology chaos is shorthand for chaotic dynamics and therefore has a different meaning from its everyday meaning of utter confusion. Chaotic dynamics is used to describe the chaotic behaviour of a chaotic system. Chaotic behaviour is not random. If the initial conditions are known with sufficient accuracy then the subsequent behaviour can, in principle, be predicted precisely. In practice, in a chaotic system the subsequent behaviour is so sensitive to the initial conditions that an attempt to reproduce the initial conditions is never sufficiently precise, and the outcome on successive attempts can vary widely.

Keywords

Chaotic System Chaotic Dynamic Chaotic Behaviour Practical Aspect Fracture Resistance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Baker GL, Blackburn JA (2005) The pendulum. A case study in physics. Oxford University Press, OxfordMATHGoogle Scholar
  2. Baker GL, Gollub JP (1996) Chaotic dynamics. An introduction, 2nd edn. Cambridge University Press, CambridgeGoogle Scholar
  3. Britten FJ (1978) The watch & clock makers’ handbook, dictionary and guide, 16th edn. Arco Publishing Company, New York (Revised by Good R)Google Scholar
  4. Burger EB, Starbird M (2005) Coincidences, chaos and all that math jazz: making light of weighty ideas. W W Norton & Company, New YorkMATHGoogle Scholar
  5. Case WB, Swanson MA (1990) The pumping of a swing from the seated position. Am J Phys 58(5):463–467CrossRefGoogle Scholar
  6. Dunkerley S (1910) Mechanisms, 3rd edn. Longmans, Green and Co., LondonGoogle Scholar
  7. Edwardes EL (1977) The story of the pendulum clock. John Sherratt & Son, AltringhamGoogle Scholar
  8. Feinstein GF (1995) M Fedchenko and his pendulum astronomical clocks. NAWCC Bull 1995:169–184Google Scholar
  9. Hall N (ed) (1992) The New Scientist guide to chaos. Penguin, LondonGoogle Scholar
  10. Huygens C (1658/1977) The horologium. Latin facsimile and English translation. In: Edwardes EL. The story of the pendulum clock. John Sherratt & Son, Altringham, pp 60–97Google Scholar
  11. Huygens C (1673/1986) Horologium oscillatorium. The pendulum clock or geometrical demonstrations concerning the motion of pendula as applied to clocks. The Iowa State University Press, Iowa (Trans by Blackwell RJ)Google Scholar
  12. Jurriaanse D (1987) The practical pendulum book, with instructions for use and thirty-eight pendulum charts. The Aquarium Press, WellingboroughGoogle Scholar
  13. Lamb H (1923) Dynamics, 2nd edn. Cambridge University Press, CambridgeMATHGoogle Scholar
  14. Lineham WJ (1914) A textbook of mechanical engineering. 11th edn. Chapman and Hall, LondonGoogle Scholar
  15. Matthews RJ (2000) Time for science education. How teaching the history and philosophy of pendulum motion can contribute to science literacy. Kluwer Academic/Plenum Publishers, New YorkGoogle Scholar
  16. Matthys R (2004) Accurate clock pendulums. Oxford University Press, OxfordCrossRefGoogle Scholar
  17. Nelson RA, Olsson MG (1986) The pendulum – rich physics from a simple system. Am J Phys 54(2):112–121CrossRefGoogle Scholar
  18. Parwani RR (2004) An approximate expression for the large angle period of a simple pendulum. Eur J Phys 25(1):37–39MATHCrossRefGoogle Scholar
  19. Patel MH and Witz JA (1991) Compliant offshore structures. Butterworth-Heinemann, OxfordGoogle Scholar
  20. Roberts D (2003) Precision pendulum clocks: 300 year quest for accurate timekeeping in England. Schiffer Publishing, AtglenGoogle Scholar
  21. Roberts D (2004) Precision pendulum clocks: France, Germany, America, and recent advancements. Schiffer Publishing, AtglenGoogle Scholar
  22. Siewert TA, Manahan MP, McCowan CN, Holt JH, Marsh FJ, and Ruth EA (2000) The history and importance of impact testing. In: Siewert TA, Manahan MP (eds) Pendulum impact testing: a century of progress. American Society for Testing and Materials, West Conshohocken, pp 3–16 (STP 1380)Google Scholar
  23. Tobin W (2003) The life and science of Léon Foucault. The man who proved that the earth rotates. Cambridge University Press, CambridgeGoogle Scholar
  24. Whitaker RJ (2001) Harmonographs I. Pendulum design. Am J Phys 69(2):162–173MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.KentUK

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