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{{Short description|Semi-ellipsoidal spinning top}}

:''For the fictional animal, see [[Rattleback (rodent)]]''.

[[File:Rattleback in action.ogv|thumb|A rattleback in action]]

A '''rattleback''' is a semi-ellipsoidal [[Spinning top|top]] which will rotate on its axis in a preferred direction. If spun in the opposite direction, it becomes unstable, "rattles" to a stop and reverses its spin to the preferred direction.

For most rattlebacks the motion will happen when the rattleback is spun in one direction, but not when spun in the other. Some exceptional rattlebacks will reverse when spun in either direction.<ref name="motivate">{{cite web|title=Boomerangs and Gyros: Introduction to Hugh's Talk |work=motivate, maths enrichment for schools, Millennium Mathematics Project |url=http://motivate.maths.org/conferences/conf14/c14_talk1.shtml |archive-url=https://web.archive.org/web/20040306062339/http://www.motivate.maths.org/conferences/conf14/c14_talk1.shtml |url-status=dead |archive-date=2004-03-06 |publisher=[[University of Cambridge]] |access-date=2013-10-19 }}</ref>

[[Image:Celt_with_gemstone_turtles-01.jpg|thumb|200px|Carved wooden rattleback]]

This counterintuitive behavior makes the rattleback a physical curiosity that has excited human imagination since prehistoric times.<ref>{{cite web |title=celt, NOUN² |work=OED: Oxford English Dictionary Online |publisher=Oxford University Press |url=https://www.oed.com/dictionary/celt_n2}}</ref>

A '''rattleback''', may also be known as a "celtanagyre", "(rebellious) [[celt (tool)|celt]]", "Celtic stone", "druid stone"rattlerocks, "rattlerock", "spinRobinson barReverser", "spin bar"Tate's," "wobble stone" (or "wobblestone,") and by the product names including "ARK", "Bizzaro Swirl"RATTLEBACKS" and, "Space Pets,Pet" isand a semi-ellipsoidal [[top]] which will spin on its axis in a preferred direction. But, if spun in the opposite direction, it becomes unstable,"Space Toy"rattles," stops and reverses its spin to the preferred direction.

:''Behold the mysterious celt,''

:''with a property that amuses.''

:''One way it will spin,''

:''the other way it refuses.''

This spin-reversal motion seems, at first sight, to violate the [[angular momentum|angular-momentum]] conservation law of physics. Moreover, for most rattlebacks, the motion will happen when the rattleback is spun in one direction, but not when spun in the other. These two peculiarities make the rattleback a physical curiosity that has excited human imagination since prehistorical times.

==History==

[[File:RATTLEBACK - ANAGYRE -(GAEL 24 inches) - Emmanuel Peluchon.jpg|thumb|Large rattleback made from different wood densities]]

Archeologists who investigated ancient [[Celt]]ic and [[Ancient Egypt|Egyptian]] [[archaeology|sites]] in the 19th century found [[celt (tool)|celts]] which exhibited the spin-reversal motion.{{citation needed|date=November 2022}} The [[antiquarian]] word ''celt'' (the "c" is soft, pronounced as "s") describes [[lithic analysis|lithic]] tools and weapons shaped like an [[adze]], [[axe]], [[chisel]], or [[hoe (tool)|hoe]].

The first modern descriptions of these celts were published in the 1890s when [[Gilbert Walker (physicist)|Gilbert Walker]] wrote his "On a curious dynamical property of celts" for the ''Proceedings of the Cambridge Philosophical Society'' in Cambridge, England, and "On a dynamical top" for the ''Quarterly Journal of Pure and Applied Mathematics'' in Somerville, Massachusetts, US.<ref>{{cite journal

Archeologists who investigated ancient [[Celt|Celtic]] and [[Ancient Egypt|Egyptian]] [[Archaeology|sites]] in the 19th century found celts which exhibited the spin-reversal motion. The [[antiquarian]] word "[[Celt (tool)|celt]]" (the "c" is pronounced as "s") describes [[adze]]-, [[axe]]-, [[chisel]]- and [[hoe]]-shaped [[Lithic analysis|lithic]] tools and weapons.

| date=1896

| last1=Walker | first1=G. T. | authorlink1=Gilbert Walker (physicist)

| title=On a dynamical top

| journal=[[The Quarterly Journal of Pure and Applied Mathematics|Quarterly Journal of Pure and Applied Mathematics]]

| volume=28

| pages=175–184

| url={{GBurl|1_zxAAAAMAAJ|p=175}} }}</ref><ref>{{cite journal

| date=1895

| last1=Walker | first1=G. T. | authorlink1=Gilbert Walker (physicist)

| title=On a curious dynamical property of celts

| journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]]

| volume=8

| issue=5

| pages=305–306

| url=https://archive.org/details/proceedingsofcam8189295camb/page/304/mode/2up}}</ref>

Additional examinations of rattlebacks were published in 1909 and 1918, and by the 1950s and 1970s, several more examinations were made. But, the popular fascination with the objects has increased notably since the 1980s when no fewer than 28 examinations were published.

The first modern descriptions of these celts were published in the 1890s when [[Gilbert Walker|Sir Gilbert Thomas Walker FRS]] wrote his "On a curious dynamical property of celts" for the ''Proceedings of the Cambridge Philosophical Society'' in Cambridge, England, and "On a dynamical top" for the ''Quarterly Journal of Pure and Applied Mathematics'' in Somerville, Mass.

==Size and materials==

Additional examinations of rattlebacks were published in 1909 and 1918, and by the 1950s and 1970s, several more examinations were made. But, the popular fascination with the objects has increased notably since the 1980s when no less than 28 examinations were published.

[[File:Celt with weights of gemstone turtles-01.jpg|thumb|Carved wooden rattleback]]

Rattleback [[artifact (archaeology)|artifact]]s are typically stone and come in various sizes. Modern ones sold as novelty puzzles and toys are generally made of plastic, wood, or glass, and come in sizes from a few inches up to {{convert|12|in}} long. A rattleback can also be made by bending a spoon.<ref>{{Cite web|url=http://www.exo.net/~pauld/TomTits2000/europetrip/technorama%20lecture/technoramalecture.html|title=Technoramalecture}}</ref>

==Size==

Two rattleback design types exist: they have either an asymmetrical base with a skewed rolling axis, or a symmetrical base with offset weighting at the ends.

While rattleback [[Artifact (archaeology)|artifact]]s are described as stone with various measurements, most which are sold currently as novelty puzzles and toys are described as plastic with measurements of 3.75-inches length x 0.75-inches width x 0.4375-inches height. Carved wooden rattlebacks are described with a measurement of 5.5-inches to 6-inches length. One plastic rattleback made and sold by Charles W. Sherburne is described with a measurement of 12-inches length. Glass rattlebacks, and those made of spoons, are described as being tested with unreported measurements. Larger rattlebacks, and those of other materials, aren't yet reported.

Two rattleback-design types exist. The first enjoys an asymmetrical base where its rolling axis is skewed. The second enjoys a symmetrical base with off-set weighting at the ends of the rattleback.

==Physics==

[[Image:Rolling-pitching.png|thumb|Rolling and pitching motions|left]]

The spin-reversal motion follows from the growth of [[flight dynamics|instabilities]] on the other rotation axes, that are rolling (on the main axis) and pitching (on the crosswise axis).<ref>{{Cite web | url=http://online.kitp.ucsb.edu/online/dynamo08/moffatt/ |date=2008 |first=Keith |last=Moffatt |publisher=Cambridge University & KITP |title=Rattleback Reversals: A Prototype of Chiral Dynamics}}</ref>

[[File:Spoon_Celt.webm|thumb|Rattleback made with spoon exhibiting multiple spin reversals.]]

[[Image:Rolling-pitching.png|thumb|200px|Rolling and pitching motions]]

When there is an asymmetry in the mass distribution with respect to the plane formed by the pitching and the vertical axes, a coupling of these two instabilities arises; one can imagine how the asymmetry in mass will deviate the rattleback when pitching, which will create some rolling.

The amplified mode will differ depending on the spin direction, which explains the rattleback's asymmetrical behavior. Depending on whether it is rather a pitching or rolling instability that dominates, the growth rate will be very high or quite low.

This explains why, due to friction, most rattlebacks appear to exhibit spin-reversal motion only when spun in the pitching-unstable direction, whilealso theyknown slowas downthe andstrong stopreversal spinningdirection. beforeWhen the rollingrattleback instability arises whenis spun in the other"stable direction", also known as the weak reversal direction, friction and damping often slow the rattleback to a stop before the rolling instability has time to fully build. Glass Some rattlebacks, however, wereexhibit reported"unstable tobehavior" exhibitedwhen this motionspun in botheither directionsdirection, and incur upseveral tosuccessive fourspin orreversals fiveper successivespin.<ref>{{cite rotationsjournal|title=Spin duringReversal aof singlethe experimentRattleback: Theory and Experiment|first1=A.|last1=Garcia|first2=M.|last2=Hubbard|date=8 July 1988|journal=Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|volume=418|issue=1854|pages=165–197|doi=10.1098/rspa.1988.0078|bibcode = 1988RSPSA.418..165G|s2cid=122747632}}</ref>

Other ways to add motion to a rattleback include tapping by pressing down momentarily on either of its ends, and rocking by pressing down repeatedly on either of its ends.

For a comprehensive analysis of rattleback's motion, see V.Ph. Zhuravlev and D.M. Klimov (2008).<ref>{{cite journal |first1=V.Ph. |last1=Zhuravlev |first2=D.M. |last2=Klimov |title=Global motion of the celt |journal=Mechanics of Solids |volume=43 |issue=3 |pages=320–7 |date=2008 |doi=10.3103/S0025654408030023 |bibcode=2008MeSol..43..320Z }}</ref> The previous papers were based on simplified assumptions and limited to studying local instability of its steady-state oscillation.

==Myths==

Realistic mathematical modelling of a rattleback is presented by G. Kudra and J. Awrejcewicz (2015).<ref>{{Cite journal|title=Application and experimental validation of new computational models of friction forces and rolling resistance|first1=Grzegorz|last1=Kudra|first2=Jan|last2=Awrejcewicz|date=September 1, 2015|journal=Acta Mechanica|volume=226|issue=9|pages=2831–2848|doi=10.1007/s00707-015-1353-z|s2cid=122992413|doi-access=free}}</ref> They focused on modelling of the contact forces and tested different versions of models of friction and rolling resistance, obtaining good agreement with the experimental results.

Rattlebacks have been misdescribed and misused as:

Numerical simulations predict that a rattleback situated on a harmonically oscillating base can exhibit rich bifurcation dynamics, including different types of periodic, quasi-periodic and chaotic motions.<ref>{{cite journal |first1=J. |last1=Awrejcewicz |first2=G. |last2=Kudra |title=Mathematical modelling and simulation of the bifurcational wobblestone dynamics |journal=Discontinuity, Nonlinearity and Complexity |volume=3 |issue=2 |pages=123–132 |date=2014 |doi=10.5890/DNC.2014.06.002 }}</ref>

*A tool of [[divination]]

==See also==

*Influenced by [[Magic (paranormal)|magic]]

*[[Spinning top]]

*[[Tesla's Egg of Columbus]]

*An expression of the object's [[Animism]]

*[[Tennis racket theorem]]

*Influenced by the [[Fourth dimension|Fourth Dimension]]

*A demonstration of [[perpetual motion]] "[[free energy]]"

*Influenced by [[Earth's magnetic field]]

*An accurate test of judicial guilt

*Influenced by the [[Coriolis effect]]

*A "Tate's" compass ("He who has a Tate's is lost.")

==References==

{{reflist|25em}}

{{refbegin}}

*Blackowiak, A. Donald. ''The dynamics of the celt with second order averaging and computer algebra''. Cornell University. Ithaca, N.Y. 1996.

*{{cite journal |first=Hermann |last=Bondi |title=The rigid body dynamics of unidirectional spin |journal=Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences |volume=405 |issue=1829 |pages=265–274 |date=1986 |doi=10.1098/rspa.1986.0052 |jstor=2397977 |bibcode=1986RSPSA.405..265B }}

*{{cite journal |first=A.B. |last=Pippard |title=How to make a celt or rattleback |journal=European Journal of Physics |volume=11 |issue=1 |pages=63–64 |date=1990 |doi=10.1088/0143-0807/11/1/112 }}

*Blackowiak, A. Donald, H. Kaplan and Richard H. Rand. "The dynamics of the celt with second order averaging and computer algebra." ''Proceedings of the ASME Design Engineering Technical Conferences''. Sacramento. 1997.

{{refend}}

*Boardman, Allan J. "The mysterious celt." ''Fine Woodworking'', 53:68-9. The Taunton Press Inc. Newtown, Conn. July/August 1985.

*[[Hermann Bondi|Bondi KCB FRS, Sir Hermann]]. "The rigid body dynamics of unidirectional spin." ''Proceedings of the Royal Society of London for the Improvement of Natural Knowledge'', A405:265-74. London. 1986.

*Caughey, T.K. "A mathematical model of the rattleback." ''International Journal of Non-Linear Mechanics'', 15:293-302. Orlando, Fla. 1980.

*Crabtree, Harold. ''An elementary treatment of the spinning tops and gyroscopic motion''. 7, 54, plate I. Longmans, Green & Co. London. 1909.

*Crane [[Doctor of Philosophy|Ph.D.]], H. Richard. "How things work: The rattleback revisited." ''The Physics Teacher'', 29(5):278-9. American Association of Physics Teachers. College Park, Md. 1991.

*Dammermann, W. "Celtic wackelsteine." ''Physics In Our Time'', 12:178-80. 1981.

*Edge [[Doctor of Philosophy|Ph.D.]], Ronald D. and Richard Lee Childers [[Doctor of Philosophy|Ph.D.]]. "String and sticky tape: Curious celts and riotous rattlebacks." ''The Physics Teacher'', 37(2):80. American Association of Physics Teachers. College Park, Md. 1999.

*Elliott, W.A. ''The inside story of the whirlygig!'' W.A. Elliott Co., Toronto.

*Elliott, W.A. ''The Tate's compass''. W.A. Elliott Co., Toronto. 1982.

*Freeman, Ira B. "What is Trevelyan's rocker?" ''The Physics Teacher'', 12:382. American Association of Physics Teachers. College Park, Md. 1974.

*Garcia, A. and M. Hubbard. "Spin reversal of the rattleback: Theory and experiment." ''Proceedings of the Royal Society of London for the Improvement of Natural Knowledge'', A418:165-97. London. 1988.

*Gray, Andrew. ''Treatise of gyrostatics and rotational motion''. Macmillan Publishers Ltd. London. 1918.

*Holzhey, C. and H. Puschmann. "The Celtic wackelstein: A remarkable gyroscope." ''Recent Science'', 1(2):6-15. 1986.

*Kane, Thomas R. and David A. Levinson. "Realistic mathematical modeling of the rattleback." ''International Journal of Non-Linear Mechanics'', 17:175-86. 1982.

*Lindberg, R.E. Jr. and R.W. Longman. "On the dynamic behavior of the wobblestone." ''Acta Mechanica'', 49:81-94. 1983.

*Magnus, Karl. "The stability of rotations of a non-symmetrical body on a horizontal surface." ''Festschrift Szabo'', 19-23, Berlin. 1971.

*Magnus, Kurt. "Zur theorie der Keltischen wackelsteine." ''Zeitschrift fuer Angewandte Mathematik und Mechanik'', 54:54-5. 1974.

*Markeev, A.P. "On the dynamics of a solid on an absolutely rough plane." ''PMM U.S.S.R'', 47:473-8. 1983.

*McGeer [[Doctor of Philosophy|Ph.D.]], Tad and Leigh Hunt Palmer [[Doctor of Philosophy|Ph.D.]] "Wobbling, toppling and forces of contact." ''American Journal of Physics'', 57:1089-98. American Association of Physics Teachers. College Park, Md. 1989.

*Moffatt [[Doctor of Philosophy|Ph.D.]] [[Royal Society|FRS]], Henry Keith. "Talk for the 50th anniversary." ''Journal of Fluid Mechanics'', Cambridge University Press. Cambridge, England. 2006.

*Pascal, M. "Asymptotic solution of the equations of motion for a Celtic stone." ''PMM U.S.S.R'', 47:269-76. 1984.

*Pascal, M. "The use of the method of averaging to study non-linear oscillations of the Celtic stone." ''PMM U.S.S.R'', 50:520-2. 1986.

*Rand, Richard H. ''Topics in nonlinear dynamics with computer algebra''. Gordon and Breach. Langhorne, Penn. 1994.

*Rand, Richard H. and Dieter Armbruster. "Perturbation methods, bifurcation theory and computer algebra." ''Springer-Verlag''. New York. 1987.

*Satterly [[Doctor of Science|D.Sc.]] [[Royal Society of Canada|FRSC]], John. "Induced rocking." ''American Journal of Physics'', 26:625-7. American Association of Physics Teachers. College Park, Md. 1958.

*Satterly [[Doctor of Science|D.Sc.]] [[Royal Society of Canada|FRSC]], John. "Rocking experiment with two degrees of freedom." ''American Journal of Physics'', 21:267-73. American Association of Physics Teachers. College Park, Md. 1953.

*Satterly [[Doctor of Science|D.Sc.]] [[Royal Society of Canada|FRSC]], John. "Three interesting instances of rocking." ''American Journal of Physics'', 23:14-26. American Association of Physics Teachers. College Park, Md. 1955.

*Satterly [[Doctor of Science|D.Sc.]] [[Royal Society of Canada|FRSC]], John. "Vibrational dynamics with lenses, mirrors and prisms." ''American Journal of Physics'', 23:562-81. American Association of Physics Teachers. College Park, Md. 1955.

*Sherburne, Charles W. "ARK: Scientific demonstration toy." ''U.S. Design 210,947''. Filed: Nov. 12, 1995. Patented: May 7, 1968. San Pedro, Calif.

*Walgate [[Doctor of Philosophy|Ph.D.]], Robert. "Tops that like to spin one way." ''Nature'', 323:204. Nature Publishing Group, London. 1986.

*[[Gilbert Walker|Walker FRS, Sir Gilbert Thomas]]. "On a curious dynamical property of celts." ''Proceedings of the Cambridge Philosophical Society'', 8:305-6. Cambridge, England. 1892/5.

*[[Gilbert Walker|Walker FRS, Sir Gilbert Thomas]]. "On a dynamical top." ''Quarterly Journal of Pure and Applied Mathematics'', 28:175-84. International Press. Somerville, Mass. 1896.

*[[Jearl Walker|Walker Ph.D., Jearl]]. "The Amateur Scientist: The mysterious 'rattleback': A stone that spins in one direction and then reverses." ''Scientific American'', 241:172-84. Scientific American Inc. New York. 1979.

*[[Jearl Walker|Walker Ph.D., Jearl]]. "The Amateur Scientist: Rattlebacks and tippe tops; Roundabout: The physics of rotation in the everyday world." ''Scientific American'', 33-8, 66. Scientific American Inc. New York. 1985.

*[[Jearl Walker|Walker Ph.D., Jearl]]. "Puzzling gyroscopes." ''Spektrum der Wissenschaft'', part 1, December, 109-13, 1979; part 2, May, 151-7, 1981.

*Wheeler [[Doctor of Philosophy|Ph.D.]], Nicholas A. ''Rattlebacks -- How do they work?'' Reed College Department of Physics. Portland, Ore.

==External links==

{{Commons category|Celtic rattlebacks}}

*4Physics.com: [http://www.4physics.com/phy_demo/rattleback.htm ''The amazing rattleback!'']

*Bondi KCB FRS, Sir Hermann. [http://links.jstor.org/sici?sici=0080-4630(19860609)405%3A1829%3C265%3ATRBDOU%3E2.0.CO%3B2-M "The rigid body dynamics of unidirectional spin."] ''Proceedings of the Royal Society of London for the Improvement of Natural Knowledge'', vol. A405, pp. 265-74. 1986.

*Brown University: [http://physics.brown.edu/physics/demopages/Demo/solids/demos/torque.html ''Torque of the devil''.] physics demonstration.

*Brown University: [http://www.physics.brown.edu/physics/demopages/Demo/solids/demos/1q6016.html ''To demonstrate a puzzling mechanical device with unidirectional rotational behavior''.] physics demonstration.

*Doherty, Paul. Scientific Explorations. [http://www.exo.net/~pauld/activities/sweden/spoonrattleback.html ''Spoon Rattleback''.] 2000.

*{{cite web |title=Celt Spoon |date=2002 |publisher=[[Flinn Scientific Inc.]] |url=http://www.flinnsci.com/Documents/demoPDFs/PhysicalSci/PS10440.pdf|archive-url=https://web.archive.org/web/20061214135407/http://www.flinnsci.com/Documents/demoPDFs/PhysicalSci/PS10440.pdf |archive-date=2006-12-14 }}

*Sanderson, Jonathan. Activity of the Week: [https://web.archive.org/web/20061021205047/http://www.scienceyear.com/about_sy/news/ps_176-200/ps_issue182.html#4 Rattleback].

*Simon Fraser University: [https://web.archive.org/web/20120205181113/http://www.sfu.ca/physics/ugrad/courses/teaching_resources/demoindex/mechanics/mech1q/celt.html ''Celt''.] physics demonstration. Burnaby, British Columbia, Canada.

*University of Cambridge Millennium Mathematics Project [https://web.archive.org/web/20120205181451/http://motivate.maths.org/conferences/conf14/c14_talk1.shtml "Boomerangs and Gyroscopes."]

{{Object manipulation}}

*Flinn Scientific Inc. [http://www.flinnsci.com/Documents/demoPDFs/PhysicalSci/PS10440.pdf "Celt Spoon."]

*Grand Illusions: [http://www.grand-illusions.com/acatalog/info_63.html ''Russian rattleback''.]

*Keath, Ed. [http://www.123too.com/ ''Turning a celt''.]

*Keltischer Wackelstein [http://www.wundersamessammelsurium.de/Mechanisches/KeltischerWackelstein "Celtic Wacklestein."]

*Krasnoukhov, Dr. Vladimir and Anatoli Kalinin. [http://www.jyuta.net/cosmo/vladimir/vladimir.html ''Stubborn Turtles''.]

*Pippard, A.B. [http://www.iop.org/EJ/abstract/0143-0807/11/1/112 "How to make a celt or rattleback."] ''European Journal of Physics'', vol. 11, pp. 63-4. Institute of Physics. 1990.

*Sanderson, Jonathan. Activity of the Week: [http://www.scienceyear.com/about_sy/news/ps_176-200/ps_issue182.html#4 Rattleback].

*Simon Fraser University: [http://www.sfu.ca/~closari/projects/ensc100/index.htm ''Rattleback''.] Engineering Science 100 Tutorial Group Nu. Burnaby, British Columbia, Canada.

*Simon Fraser University: [http://www.sfu.ca/physics/ugrad/courses/teaching_resources/demoindex/mechanics/mech1q/celt.html ''Celt''.] physics demonstration. Burnaby, British Columbia, Canada.

*Singmaster, David. [http://www.g4g4.com/MyCD5/SOURCES/SOURCE4.DOC ''Celts -- Rattlebacks''.] South Bank University. London. 2004.

*Toys From Times Past [http://www.toysfromtimespast.com/toys/stone.htm "Wobble Stone."]

*University of Cambridge Millennium Mathematics Project [http://motivate.maths.org/conferences/conf14/c14_talk1.shtml "Boomerangs and Gyroscopes."]

[[de:Keltischer Wackelstein]]

[[pl:Kamień celtycki]]

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