Pendulum (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Pendulum" in English language version.

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17centurymaths.com

defined by Christiaan Huygens: Huygens, Christian (1673). "Horologium Oscillatorium" (PDF). 17centurymaths. 17thcenturymaths.com. Retrieved 2009-03-01., Part 4, Definition 3, translated July 2007 by Ian Bruce
Huygens, Christian (1673). "Horologium Oscillatorium". 17centurymaths. Translated by Bruce, Ian. 17thcenturymaths.com. Retrieved 2009-03-01., Part 4, Proposition 5
Huygens (1673) Horologium Oscillatorium, Part 4, Proposition 20
Huygens, Christian; translated by Ian Bruce (July 2007). "Horologium Oscillatorium" (PDF). 17centurymaths. 17thcenturymaths.com. Retrieved 2009-03-01.
Huygens, Horologium Oscillatorium, Part 2, Proposition 25

aip.org

scitation.aip.org

Nauenberg, Michael (2004). "Hooke and Newton: Divining Planetary Motions". Physics Today. 57 (2): 13. Bibcode:2004PhT....57b..13N. doi:10.1063/1.1688052. Retrieved 2007-05-30.

antique-horology.org

"...it is affected by either the intemperance of the air or any faults in the mechanism so the crutch QR is not always activated by the same force... With large arcs the swings take longer, in the way I have explained, therefore some inequalities in the motion of the timepiece exist from this cause...", Huygens, Christiaan (1658). Horologium (PDF). The Hague: Adrian Vlaqc., translation by Ernest L. Edwardes (December 1970) Antiquarian Horology, Vol.7, No.1
Huygens, Christiaan (1658). Horologium (PDF). The Hague: Adrian Vlaqc., translation by Ernest L. Edwardes (December 1970) Antiquarian Horology, Vol.7, No.1

archive.org

Morris, William, Ed. (1979). The American Heritage Dictionary, New College Ed. New York: Houghton-Mifflin. p. 969. ISBN 978-0-395-20360-6.{{cite book}}: CS1 maint: multiple names: authors list (link)
Halliday, David; Robert Resnick; Jearl Walker (1997). Fundamentals of Physics, 5th Ed. New York: John Wiley & Sons. p. 381. ISBN 978-0-471-14854-8.
Glasgow, David (1885). Watch and Clock Making. London: Cassel & Co. p. 278.
Newton, Roger G. (2004). Galileo's Pendulum: From the Rhythm of Time to the Making of Matter. US: Harvard University Press. p. 52. ISBN 978-0-674-01331-5.
Akyeampong, Emmanuel K.; Gates, Henry Louis Jr., eds. (2012). "Ibn Yunus". Dictionary of African Biography. Vol. 3. Oxford Univ. Press. pp. 126–127. ISBN 978-0-19-538207-5.
Galilei, Galileo (1909). Favaro, Antonio [in Italian] (ed.). Le Opere di Galileo Galilei, Edizione Nazionale [The Works of Galileo Galilei, National Edition] (in Italian). Florence: Barbera. ISBN 978-88-09-20881-0. {{cite book}}: ISBN / Date incompatibility (help)
Poynting, John Henry; Joseph John Thompson (1907). A Textbook of Physics, 4th Ed. London: Charles Griffin & Co. pp. 20–22.
Glasgow, David (1885). Watch and Clock Making. London: Cassel & Co. pp. 279–284.
Glasgow 1885, p.282
Poynting, John Henry; Joseph John Thompson (1907). A Textbook of Physics, 4th Ed. London: Charles Griffin & Co. p. 20.
Poynting, John Henry (1894). The Mean Density of the Earth. London: Charles Griffin. pp. 22–24.
Cox, John (1904). Mechanics. Cambridge, UK: Cambridge Univ. Press. pp. 311–312.
Poynting, John Henry (1894). The Mean Density of the Earth. London: Charles Griffin & Co. pp. 24–29.
Renwick, James (1832). The Elements of Mechanics. Philadelphia: Carey & Lea. pp. 286–287.
Zupko, 1990, p.131
Zupko, 1990, p.140-141
Zupko, 1990, p.93
Roth, Cecil (1964). The Spanish Inquisition. W. W. Norton and Company. pp. 258. ISBN 978-0-393-00255-3. pendulum. {{cite book}}: ISBN / Date incompatibility (help)

arxiv.org

Agnoli, Paolo; Giulio D'Agostini (December 2004). "Why does the meter beat the second?". arXiv:physics/0412078.

bnf.fr

gallica.bnf.fr

Picard, Jean (1671). La Mesure de la Terre [The Measurement of the Earth] (in French). Paris, France: Imprimerie Royale. p. 4. Picard described a pendulum consisting of a copper ball which was an inch (2.54 mm) in diameter and was suspended by a strand of pite, a fiber from the aloe plant. Picard then mentions that temperature slightly effects the length of this pendulum: "Il est vray que cette longueur ne s'est pas toûjours trouvées si précise, & qu'il a semblé qu'elle devoit estre toûjours un peu accourcie en Hyver, & allongée en esté; mais c'est seulement de la dixieme partie d'une ligne ..." ("It is true that this length [of the pendulum] is not always found [to be] so precise, and that it seemed that it should be always a bit shortened in winter, and lengthened in summer; but it is only by a tenth part of a line ...") [1 ligne (line) = 2.2558 mm].

books.google.com

Cooper, Herbert J. (2007). Scientific Instruments. New York: Hutchinson's. p. 162. ISBN 978-1-4067-6879-4.
Good, Gregory (1998). Sciences of the Earth: An Encyclopedia of Events, People, and Phenomena. Routledge. p. 394. ISBN 978-0-8153-0062-5.
"ibn+yunus"+pendulum&pg=RA2-PA126 "Pendulum". Encyclopedia Americana. Vol. 21. The Americana Corp. 1967. p. 502. ISBN 978-0-19-538207-5. Retrieved 2009-02-20.
Baker, Cyril Clarence Thomas (1961). Dictionary of Mathematics. G. Newnes. p. 176.
Matthews, Michael R. (2000). Time for science education. Springer. p. 87. ISBN 978-0-306-45880-4.
Drake, Stillman (2003). Galileo at Work: His scientific biography. USA: Courier Dover. pp. 20–21. ISBN 978-0-486-49542-2.
Drake, Stillman (2003). Galileo at Work: His scientific biography. USA: Courier Dover. p. 17. ISBN 978-0-486-49542-2.
Murdin, Paul (2008). Full Meridian of Glory: Perilous Adventures in the Competition to Measure the Earth. Springer. p. 41. ISBN 978-0-387-75533-5.
La Lampada di Galileo, by Francesco Malaguzzi Valeri, for Archivio storico dell'arte, Volume 6 (1893); Editor, Domenico Gnoli; Publisher Danesi, Rome; Page 215-218.
Drake 2003, p.419–420
although there are unsubstantiated references to prior pendulum clocks made by others: Usher, Abbott Payson (1988). A History of Mechanical Inventions. Courier Dover. pp. 310–311. ISBN 978-0-486-25593-4.
Eidson, John C. (2006). Measurement, Control, and Communication using IEEE 1588. Burkhausen. p. 11. ISBN 978-1-84628-250-8.
Lenzen, Victor F.; Robert P. Multauf (1964). "Paper 44: Development of gravity pendulums in the 19th century". United States National Museum Bulletin 240: Contributions from the Museum of History and Technology reprinted in Bulletin of the Smithsonian Institution. Washington: Smithsonian Institution Press. p. 307. Retrieved 2009-01-28.
Richer, Jean (1679). Observations astronomiques et physiques faites en l'isle de Caïenne. Mémoires de l'Académie Royale des Sciences. Bibcode:1679oaep.book.....R. cited in Lenzen & Multauf, 1964, p.307
Lenzen & Multauf, 1964, p.307
Matthews, Michael R. (1994). Science Teaching: The Role of History and Philosophy of Science. Psychology Press. pp. 121–122. ISBN 978-0-415-90899-3.
Bevilaqua, Fabio; Lidia Falomo; Lucio Fregonese; Enrico Gianetto; Franco Giudise; Paolo Mascheretti (2005). "The pendulum: From constrained fall to the concept of potential". The Pendulum: Scientific, Historical, Philosophical, and Educational Perspectives. Springer. pp. 195–200. ISBN 1-4020-3525-X. Retrieved 2008-02-26. gives a detailed description of Huygens' methods
Andrewes, W.J.H. Clocks and Watches: The leap to precision in Macey, Samuel (1994). Encyclopedia of Time. Taylor & Francis. pp. 123–125. ISBN 978-0-8153-0615-3.
Usher, 1988, p.312
Beckett, Edmund (1874). A Rudimentary Treatise on Clocks and Watches and Bells, 6th Ed. London: Lockwood & Co. p. 50.
Graham, George (1726). "A contrivance to avoid irregularities in a clock's motion occasion'd by the action of heat and cold upon the rod of the pendulum". Philosophical Transactions of the Royal Society. 34 (392–398): 40–44. doi:10.1098/rstl.1726.0006. S2CID 186210095. cited in Day, Lance; Ian McNeil (1996). Biographical Dictionary of the History of Technology. Taylor & Francis. p. 300. ISBN 978-0-415-06042-4.
Kater, Henry (1818). "An account of experiments for determining the length of the pendulum vibrating seconds in the latitude of London". Phil. Trans. R. Soc. 104 (33): 109. Retrieved 2008-11-25.
Amir Aczel (2003) Leon Foucault: His life, times and achievements, in Matthews, Michael R.; Colin F. Gauld; Arthur Stinner (2005). The Pendulum: Scientific, Historical, Educational, and Philosophical Perspectives. Springer. p. 177. ISBN 978-1-4020-3525-8.
Tobin, William (2003). The Life and Science of Leon Foucault: The man who proved the Earth rotates. UK: Cambridge University Press. pp. 148–149. ISBN 978-0-521-80855-2.
Jones, Tony (2000). Splitting the Second: The Story of Atomic Time. CRC Press. p. 30. ISBN 978-0-7503-0640-9.
Kaler, James B. (2002). Ever-changing Sky: A Guide to the Celestial Sphere. UK: Cambridge Univ. Press. p. 183. ISBN 978-0-521-49918-7.
Audoin, Claude; Bernard Guinot; Stephen Lyle (2001). The Measurement of Time: Time, Frequency, and the Atomic Clock. UK: Cambridge Univ. Press. p. 83. ISBN 978-0-521-00397-1.
Torge, Wolfgang (2001). Geodesy: An Introduction. Walter de Gruyter. p. 177. ISBN 978-3-11-017072-6.
Matthys, Robert J. (2004). Accurate Pendulum Clocks. UK: Oxford Univ. Press. p. 4. ISBN 978-0-19-852971-2.
Mattheys, 2004, p. 13
Matthys 2004, p.91-92
Beckett 1874, p.48
Beckett 1874, p.43
Matthys 2004, p.3
Matthys 2004, p.7-12
Matthys 2004, Part 3, p.153-179
Poynting & Thompson, 1907, p.13-14
Updegraff, Milton (February 7, 1902). "On the measurement of time". Science. 15 (371): 218–219. doi:10.1126/science.ns-15.374.218-a. PMID 17793345. S2CID 21030470. Retrieved 2009-07-13.
Dunwoody, Halsey (1917). Notes, Problems, and Laboratory Exercises in Mechanics, Sound, Light, Thermo-Mechanics and Hydraulics, 1st Ed. New York: John Wiley & Sons. p. 87.
Jespersen, James; Fitz-Randolph, Jane; Robb, John (1999). From Sundials to Atomic Clocks: Understanding Time and Frequency. New York: Courier Dover. pp. 41–50. ISBN 978-0-486-40913-9. p.39
Matthys, Robert J. (2004). Accurate Pendulum Clocks. UK: Oxford Univ. Press. pp. 27–36. ISBN 978-0-19-852971-2. has an excellent comprehensive discussion of the controversy over the applicability of Q to the accuracy of pendulums.
Matthys, 2004, p.32, fig. 7.2 and text
Matthys, 2004, p.81
Airy, George Biddle (November 26, 1826). "On the Disturbances of Pendulums and Balances and on the Theory of Escapements". Transactions of the Cambridge Philosophical Society. 3 (Part 1): 105. Retrieved 2008-04-25.
Beckett 1874, p.75-79
Poynting & Thompson 1907, p.9
Victor F., Lenzen; Robert P. Multauf (1964). "Paper 44: Development of gravity pendulums in the 19th century". United States National Museum Bulletin 240: Contributions from the Museum of History and Technology reprinted in Bulletin of the Smithsonian Institution. Washington: Smithsonian Institution Press. p. 307. Retrieved 2009-01-28.
Poynting & Thompson, 1907, p.10
Poynting & Thomson 1904, p.23
Lenzen & Multauf 1964, p.320
Poynting & Thompson 1907, p.18
Lenzen & Multauf 1964, p.324
Lenzen & Multauf 1964, p.329
Woolard, George P. (June 28–29, 1957). "Gravity observations during the IGY". Geophysics and the IGY: Proceedings of the symposium at the opening of the International Geophysical Year. Washington, D.C.: American Geophysical Union, Nat'l Academy of Sciences. p. 200. Retrieved 2009-05-27.
Lenzen & Multauf 1964, p.336, fig.28
Michael R., Matthews (2001). "Methodology and Politics in Science: The fate of Huygens 1673 proposal of the pendulum as an international standard of length and some educational suggestions". Science, Education, and Culture: The contribution of history and philosophy of science. Springer. p. 296. ISBN 0-7923-6972-6.
Alder, Ken (2003). The measure of all things: The seven-year odyssey and hidden error that transformed the world. US: Simon and Schuster. p. 88. ISBN 978-0-7432-1676-0.
quoted in LeConte, John (August 1885). "The Metric System". The Overland Monthly. 6 (2): 178. Retrieved 2009-03-04.
Schumacher, Heinrich (1821). "Danish standard of length". The Quarterly Journal of Science, Literature and the Arts. 11 (21): 184–185. Retrieved 2009-02-17.
"Schumacher, Heinrich Christian". The American Cyclopedia. Vol. 14. D. Appleton & Co., London. 1883. p. 686. Retrieved 2009-02-17.
Trautwine, John Cresson (1907). The Civil Engineer's Pocket-Book, 18th Ed. New York: John Wiley. p. 216.
Sorenson, Roy (2014). "Novice Thought Experiments". In Booth, Anthony Robert; Rowbottom, Darrell P. (eds.). Intuitions. Oxford Univ Pr. p. 139. ISBN 9780199609192. Retrieved 15 March 2017.
Scott, George Ryley (2009). The History Of Torture Throughout the Ages. Routledge. p. 242. ISBN 978-1136191602.
Llorente, Juan Antonio (1826). The history of the Inquisition of Spain. Abridged and translated by George B. Whittaker. Oxford University. pp. XX, preface.
Poe, Edgar Allan (1842). The Pit and the Pendulum. Booklassic. ISBN 978-9635271900. {{cite book}}: ISBN / Date incompatibility (help)
Mannix, Daniel P. (2014). The History of Torture. eNet Press. p. 76. ISBN 978-1-61886-751-3.
Pavlac, Brian (2009). Witch Hunts in the Western World: Persecution and Punishment from the Inquisition through the Salem Trials. ABC-CLIO. p. 152. ISBN 978-0-313-34874-7.

chalmers.se

fy.chalmers.se

Nelson, Robert; M. G. Olsson (February 1987). "The pendulum – Rich physics from a simple system" (PDF). American Journal of Physics. 54 (2): 112–121. Bibcode:1986AmJPh..54..112N. doi:10.1119/1.14703. S2CID 121907349. Retrieved 2008-10-29.

clockvault.com

"The Reifler and Shortt clocks". JagAir Institute of Time and Technology. Retrieved 2009-12-29.

colostate.edu

math.colostate.edu

Bevivino, Josh (2009). "The Path From the Simple Pendulum to Chaos" (PDF). Department of Physics, Colorado State University. Retrieved 4 May 2025.

doi.org

Marrison, Warren (1948). "The Evolution of the Quartz Crystal Clock". Bell System Technical Journal. 27 (3): 510–588. doi:10.1002/j.1538-7305.1948.tb01343.x. Archived from the original on 2011-07-17.
Nelson, Robert; M. G. Olsson (February 1987). "The pendulum – Rich physics from a simple system" (PDF). American Journal of Physics. 54 (2): 112–121. Bibcode:1986AmJPh..54..112N. doi:10.1119/1.14703. S2CID 121907349. Retrieved 2008-10-29.
Deschaine, J. S.; Suits, B. H. (2008). "The hanging cord with a real tip mass". European Journal of Physics. 29 (6): 1211–1222. Bibcode:2008EJPh...29.1211D. doi:10.1088/0143-0807/29/6/010. S2CID 122637957.
Levien, R. B.; Tan, S. M. (1993). "Double Pendulum: An experiment in chaos". American Journal of Physics. 61 (11): 1038. Bibcode:1993AmJPh..61.1038L. doi:10.1119/1.17335.
Hall, Bert S. (September 1978). "The scholastic pendulum". Annals of Science. 35 (5): 441–462. doi:10.1080/00033797800200371. ISSN 0003-3790.
Nauenberg, Michael (2004). "Hooke and Newton: Divining Planetary Motions". Physics Today. 57 (2): 13. Bibcode:2004PhT....57b..13N. doi:10.1063/1.1688052. Retrieved 2007-05-30.
Graham, George (1726). "A contrivance to avoid irregularities in a clock's motion occasion'd by the action of heat and cold upon the rod of the pendulum". Philosophical Transactions of the Royal Society. 34 (392–398): 40–44. doi:10.1098/rstl.1726.0006. S2CID 186210095. cited in Day, Lance; Ian McNeil (1996). Biographical Dictionary of the History of Technology. Taylor & Francis. p. 300. ISBN 978-0-415-06042-4.
Oprea, John (1995). "Geometry and the Focault Pendulum" (PDF). The American Mathematical Monthly. 102 (6). Mathematical Association of America: 515–522. doi:10.1080/00029890.1995.12004611. Archived (PDF) from the original on 2022-10-09. Retrieved 13 April 2021.
Updegraff, Milton (February 7, 1902). "On the measurement of time". Science. 15 (371): 218–219. doi:10.1126/science.ns-15.374.218-a. PMID 17793345. S2CID 21030470. Retrieved 2009-07-13.
Harper, William L. (Dec 2011). "Christiaan Huygens: A Great Natural Philosopher Who Measured Gravity and an Illuminating Foil for Newton on Method". Isaac Newton's Scientific Method: Turning Data into Evidence about Gravity and Cosmology. pp. 194–219. doi:10.1093/acprof:oso/9780199570409.003.0005. ISBN 978-0-19-957040-9.
A.L. Fradkov; B. Andrievsky (2007). "Synchronization and phase relations in the motion of two-pendulum system". International Journal of Non-linear Mechanics. 42 (6): 895–901. Bibcode:2007IJNLM..42..895F. doi:10.1016/j.ijnonlinmec.2007.03.016.
Yurchenko, D.; Alevras, P. (2013). "Dynamics of the N-pendulum and its application to a wave energy converter concept". International Journal of Dynamics and Control. 1 (4): 4. doi:10.1007/s40435-013-0033-x.

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geocities.com

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ghostarchive.org

Oprea, John (1995). "Geometry and the Focault Pendulum" (PDF). The American Mathematical Monthly. 102 (6). Mathematical Association of America: 515–522. doi:10.1080/00029890.1995.12004611. Archived (PDF) from the original on 2022-10-09. Retrieved 13 April 2021.
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Nelson, Robert; M. G. Olsson (February 1987). "The pendulum – Rich physics from a simple system" (PDF). American Journal of Physics. 54 (2): 112–121. Bibcode:1986AmJPh..54..112N. doi:10.1119/1.14703. S2CID 121907349. Retrieved 2008-10-29.
Deschaine, J. S.; Suits, B. H. (2008). "The hanging cord with a real tip mass". European Journal of Physics. 29 (6): 1211–1222. Bibcode:2008EJPh...29.1211D. doi:10.1088/0143-0807/29/6/010. S2CID 122637957.
Levien, R. B.; Tan, S. M. (1993). "Double Pendulum: An experiment in chaos". American Journal of Physics. 61 (11): 1038. Bibcode:1993AmJPh..61.1038L. doi:10.1119/1.17335.
Nauenberg, Michael (2004). "Hooke and Newton: Divining Planetary Motions". Physics Today. 57 (2): 13. Bibcode:2004PhT....57b..13N. doi:10.1063/1.1688052. Retrieved 2007-05-30.
Richer, Jean (1679). Observations astronomiques et physiques faites en l'isle de Caïenne. Mémoires de l'Académie Royale des Sciences. Bibcode:1679oaep.book.....R. cited in Lenzen & Multauf, 1964, p.307
A.L. Fradkov; B. Andrievsky (2007). "Synchronization and phase relations in the motion of two-pendulum system". International Journal of Non-linear Mechanics. 42 (6): 895–901. Bibcode:2007IJNLM..42..895F. doi:10.1016/j.ijnonlinmec.2007.03.016.

sciencedemonstrations.fas.harvard.edu

Harvard Natural Sciences Lecture Demonstrations, Pendulum Waves

ieee-uffc.org

Marrison, Warren (1948). "The Evolution of the Quartz Crystal Clock". Bell System Technical Journal. 27 (3): 510–588. doi:10.1002/j.1538-7305.1948.tb01343.x. Archived from the original on 2011-07-17.

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Bigotti, Fabrizio; Taylor, David (2017). "The Pulsilogium of Santorio: New Light on Technology and Measurement in Early Modern Medicine". Societate Si Politica. 11 (2): 53–113. ISSN 1843-1348. PMC 6407692. PMID 30854144.
Updegraff, Milton (February 7, 1902). "On the measurement of time". Science. 15 (371): 218–219. doi:10.1126/science.ns-15.374.218-a. PMID 17793345. S2CID 21030470. Retrieved 2009-07-13.

ncbi.nlm.nih.gov

Bigotti, Fabrizio; Taylor, David (2017). "The Pulsilogium of Santorio: New Light on Technology and Measurement in Early Modern Medicine". Societate Si Politica. 11 (2): 53–113. ISSN 1843-1348. PMC 6407692. PMID 30854144.

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