Rattleback

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For the fictional animal, see Rattleback (rodent).
Carved wooden rattleback

A rattleback, also known as an "anagyre", "celt", "Celtic stone", "rebellious celt", "rattlerock", "spin bar", "wobble stone" or "wobblestone" and by the product names "ARK," "Bizzaro Swirls," "RATTLEBACKS," "Space Pet" and "Space Toy," is a semi-ellipsoidal top which will spin on its axis in a preferred direction. But, if spun in the opposite direction, it becomes unstable, "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.
Rattleback in action.ogg

This spin-reversal motion seems, at first sight, to violate the 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. Some exceptional rattlebacks will reverse when spun in either direction. [1] [2] [3] This makes the rattleback a physical curiosity that has excited human imagination since prehistorical times.

Contents

[edit] History

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

The first modern descriptions of these celts were published in the 1890s when 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.

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.

[edit] Size and Materials

While rattleback artifacts 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[1], are described as being tested with unreported measurements. Larger rattlebacks, and those of other materials, aren't yet reported.

Two rattleback-design types exist. They have either an asymmetrical base where its rolling axis is skewed, or symmetrical base, with off-set weighting at the ends.

[edit] Physics

The spin-reversal motion follows from the growth of instabilities on the other rotation axes, that are rolling (on the main axis) and pitching (on the crosswise axis).

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 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 exhibit spin-reversal motion only when spun in the pitching-unstable direction, while they slow down and stop spinning before the rolling instability arises when spun in the "stable" direction. Also, after stopping, the spin in the "stable" direction is considerably slower than the original spin speed. Some rattlebacks, however, exhibit "unstable behavior" when spun in either direction, and incur several successive spin reversals per spin.[4]

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.

[edit] Video

[edit] Myths

 This section does not cite any references or sources. Please help improve this article by adding citations to reliable sources (ideally, using inline citations). Unsourced material may be challenged and removed. (August 2008)

Rattlebacks have been misdescribed and misused as:

  • An expression of the object's Animism
  • An accurate test of judicial guilt
  • A "Tate's" compass ("He who has a Tate's is lost.")

[edit] See also

[edit] References

  1. ^ Motivate - Mathematics Videoconferences for Schools
  2. ^ Institut of Mechatronics, Chemnitz, Germany
  3. ^ Turning a celt - Keath, Ed.
  4. ^ The Smithsonian/NASA Astrophysics Data System
  • Blackowiak, A. Donald. The dynamics of the celt with second order averaging and computer algebra. Cornell University. Ithaca, N.Y. 1996.
  • 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.
  • Boardman, Allan J. "The mysterious celt." Fine Woodworking, 53:68-9. The Taunton Press Inc. Newtown, Conn. July/August 1985.
  • 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 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 Ph.D., Ronald D. and Richard Lee Childers 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.
  • 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 Ph.D., Tad and Leigh Hunt Palmer 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 Ph.D. 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 D.Sc. FRSC, John. "Induced rocking." American Journal of Physics, 26:625-7. American Association of Physics Teachers. College Park, Md. 1958.
  • Satterly D.Sc. 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 D.Sc. FRSC, John. "Three interesting instances of rocking." American Journal of Physics, 23:14-26. American Association of Physics Teachers. College Park, Md. 1955.
  • Satterly D.Sc. 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 Ph.D., Robert. "Tops that like to spin one way." Nature, 323:204. Nature Publishing Group, London. 1986.
  • 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.
  • Walker FRS, Sir Gilbert Thomas. "On a dynamical top." Quarterly Journal of Pure and Applied Mathematics, 28:175-84. International Press. Somerville, Mass. 1896.
  • 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.
  • 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.
  • Walker Ph.D., Jearl. "Puzzling gyroscopes." Spektrum der Wissenschaft, part 1, December, 109-13, 1979; part 2, May, 151-7, 1981.
  • Wheeler Ph.D., Nicholas A. Rattlebacks -- How do they work? Reed College Department of Physics. Portland, Ore.

[edit] External links

  • Simon Fraser University: Rattleback. Engineering Science 100 Tutorial Group Nu. Burnaby, British Columbia, Canada.
  • Simon Fraser University: Celt. physics demonstration. Burnaby, British Columbia, Canada.
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