Abstract
Kuhn underlined the relevance of Galileo’s gestalt switch in the interpretation of a swinging body: from constrained fall to time metre. But the new interpretation did not eliminate the older one. The constrained fall, both in the motion of pendulums and along inclined planes, led Galileo to the law of free fall. Experimenting with physical pendulums and assuming the impossibility of perpetual motion Huygens obtained a law of conservation of vis viva at specific positions, beautifully commented by Mach. Daniel Bernoulli generalised Huygens results introducing the concept of potential and the related independence of the ‘work’ done from the trajectories (paths) followed: vis viva conservation at specific positions is now linked with the potential. Feynman’s modern way of teaching the subject shows striking similarities with Bernoulli’s approach. A number of animations and simulations can help to visualise and teach some of the pendulum’s interpretations related to what we now see as instances of energy conservation.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bernoulli, D.: 1738, Hydrodynamica, sive de viribus et motibus fluidorum commentarii, Argentorati, Basel.
Bernoulli, D.: 1748, ‘Remarques sur le principe de la conservation des forces vives pris dans un sens gé néral’, in Lindsay 1975, pp. 143–148.
Camerota, M.: 1992, Gli scritti De motu antiquiora di Galileo Galilei: il Ms Gal 7, CUEC, Cagliari.
Drake, S.: 1976, ‘The Evolution of De Motu’, Physis 14, 321–348.
Drake, S.: 1995, Galileo at Work, Reprinted, Dover Publication, New York.
Erlichson, H.: 1996, ‘Christiaan Huygens’ Discovery of the Center of Oscillation Formula’, American Journal of Physics, 64, 571–574.
Feynman, R.P., Leighton, R.B. & Sands, M.: 1975, The Feynman Lectures on Physics, Inter European Editions, Amsterdam.
Gabbey, A.: 1980, ‘Huygens and Mechanics’, in H.J.M., Bos, M.J.S. Rudwick and R.P.W. Visser. (eds.), Studies on Christiaan Huygens, Swets and Zeitlinger, Lisse, pp. 166–199.
Galilei, G.: 1890–1909a, ‘De Motu’, in Le opere di Galileo Galilei, Edizione Nazionale, Vol. 1, Barbera, Firenze.
Galilei, G.: 1890–1909b, ‘Discorsi e dimostrazioni matematiche intorno a due nuove scienze’, in Le opere di Glileo Galilei, Edizione Nazionale, Vol. 8, Barbera, Firenze.
Galilei, G.: 1890–1909c, ‘Mecaniche’, in Le opere di Galileo Galilei, Edizione Nazionale, Vol. 2, Barbera, Firenze.
Galilei, G.: 1954, Dialogues Concerning Two New Sciences, trans. H. Crew and A.D. Salvio, Dover Publications, New York.
Galilei, G.: 1960, Galileo Galilei On Motion and On Mechanics, trans. I.E. Drabkin and S. Drake, University of Wisconsin Press, Madison.
Galluzzi, P.: 1979, Momento: studi galileiani, Edizioni dell’ Ateneo e Bizzarri, Roma.
Gamow, G.: 1961, Biography of Physics, Harper and Row, New York.
Huygens, C.: 1888–1950, ‘Orologium oscillatorium’, in Oeuvres complètes de Christiaan Huygens, Vol. 18, M. Nijho., La Haye.
Huygens, C.: 1986, The Pendulum Clock or Geometrical Demonstrations Concerning the Motion of Pendula as Applied to Clocks, trans. R.J. Blackwell, The Iowa State University Press, Ames.
Koyré, A.: 1978, Galileo Studies, trans. J. Mepham and Mepham, Hassocks.
Kuhn, T.: 1970, The Structure of Scientific Revolutions, 2nd edn. University of Chicago Press, Chicago.
Lindsay, R.B.: 1975, Energy: Historical Developement of the Concept, Dowden, Hutchinson and Ross, Stroudsburg.
MacCurdy, E. (ed.): 1941, The Notebooks of Leonardo da Vinci, Garden City Publishing Co., New York.
Mach, E.: 1974, The Science of Mechanics: A Critical and Historical Account of its Development, trans. T.J. McCormack, The Open Court Publishing Company, La Salle.
Matthews, M.: 2000, Times for Science Education, Kluwer, New York.
Naylor, R.: 1974, ‘Galileo and the Problem of Free Fall’, British Journal for the History of Science 7, 105–134.
Wisan, W.L.: 1974, ‘The New Science of Motion: A Study of Galileo’s De Motu locali’, Archive for History of Exact Sciences 13, 103–306.
Yoder, J.G.: 1988, Unrolling Time: Christiaan Huygens and the Mathematization of Nature, Cambridge University Press, Cambridge.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer
About this chapter
Cite this chapter
Bevilacqua, F., Falomo, L., Fregonese, L., Giannetto, E., Giudice, F., Mascheretti, P. (2005). The Pendulum: From Constrained Fall to the Concept of Potential. In: Matthews, M.R., Gauld, C.F., Stinner, A. (eds) The Pendulum. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3526-8_14
Download citation
DOI: https://doi.org/10.1007/1-4020-3526-8_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3525-8
Online ISBN: 978-1-4020-3526-5
eBook Packages: Humanities, Social Sciences and LawEducation (R0)