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Pbsouthwood (talk | contribs) Changing short description from "Semi-ellipsoidal top" to "Semi-ellipsoidal spinning top" (Shortdesc helper) |
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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.
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For a comprehensive analysis of rattleback's motion, see V.Ph. Zhuravlev and D.M. Klimov (2008).<ref>V.Ph. Zhuravlev and D.M. Klimov, Global motion of the celt, ''Mechanics of Solids'', 2008, Vol. 43, No. 3, pp. 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}}</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>J. Awrejcewicz, G. Kudra, Mathematical modelling and simulation of the bifurcational wobblestone dynamics, ''Discontinuity, Nonlinearity and Complexity'', 3(2), 2014, 123-132.</ref>
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