Rattleback: Difference between revisions

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

[[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.

This spin-reversal appears to violate the law of the [[angular momentum#Conservation of angular momentum|conservation of angular momentum]]. Moreover, forFor 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>

This counterintuitive behavior makes the rattleback a physical curiosity that has excited human imagination since prehistoric times.<ref>"{{cite web |title=celt, n.NOUN^2". |work=OED: Online.Oxford SeptemberEnglish 2012.Dictionary Online |publisher=Oxford University Press. 1 October 2012 <http|url=https://www.oed.com/viewdictionary/Entry/29533?isAdvanced=false&result=2&rskey=EPfrjA&>celt_n2}}</ref>

A rattleback may also be known as a "anagyre", "(rebellious) [[celt (tool)|celt]]", "Celtic stone", "druid stone", "rattlerock", "Robinson Reverser", "spin bar", "wobble stone" (or "wobblestone") and by product names including "ARK", "Bizzaro Swirl", "Space Pet" and "Space Toy".

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==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.{{cncitation 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

| 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.

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==Size and materials==

[[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 inches|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> Larger rattlebacks (up to 8 feet long and 16 inches wide) are made on request by Emmanuel Peluchon for science museums.<ref>{{cite web|url=http://boisselier.ca/en/products-page/curiosities/|title=Rattlebacks, puzzles and musical tree by Emmanuel Peluchon|website=boisselier.ca}}</ref>

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

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.

==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 title|first=Keith |last=Moffatt, |publisher=Cambridge Univ.University & KITP, |title=Rattleback Reversals: A Prototype of Chiral Dynamics}}</ref>

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

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.

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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, also known as the strong reversal direction. When the rattleback is spun in the "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. Some rattlebacks, however, exhibit "unstable behavior" when spun in either direction, and incur several successive spin reversals per spin.<ref>{{cite journal|title=Spin Reversal of the Rattleback: 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 and |first2=D.M. |last2=Klimov, |title=Global motion of the celt, ''|journal=Mechanics of Solids'', |volume=43 |issue=3 |pages=320–7 |date=2008, Vol|doi=10.3103/S0025654408030023 |bibcode=2008MeSol..43, No. 3, pp.320Z 320-327.}}</ref> The previous papers were based on simplified assumptions and limited to studying local instability of its steady-state oscillation.

Realistic mathematical modelling of a rattleback is presented by G. Kudra and J. Awrejcewicz (2015).<ref>{{Cite journal|url=https://doi.org/10.1007/s00707-015-1353-z|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|via=Springer Link|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.

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, 123-132|doi=10.5890/DNC.2014.06.002 }}</ref>

==See also==

*[[Spinning top]]

*[[Tesla's Egg of Columbus]]

*[[Tennis racket theorem]]

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==References==

{{reflist|25em}}

{{refbegin}}

*{{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 }}

{{refend}}

==External links==

{{Commons category|Celtic rattlebacks}}

*Bondi, Hermann. [https://www.jstor.org/stable/2397977 "The rigid body dynamics of unidirectional spin."] ''Proceedings of the Royal Society of London for the Improvement of Natural Knowledge'', vol. A405, pp.&nbsp;265–74. 1986.

*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 "Celt|archive-date=2006-12-14 Spoon."]}}

*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.&nbsp;63–4. Institute of Physics. 1990.

*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.

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[[Category:Educational toys]]

[[Category:Articles containing video clips]]

[[Category:TopsSpinning tops]]

[[Category:Classical mechanics]]