Nøgleord
Snurretop
Tippetoppen
Citation/Eksport
Resumé
Klaus Seiersen analyserer den klassiske “tippetop”, der spontant vender sig under rotation og dermed udfordrer intuitionen om bevarelse af energi og impulsmoment. Artiklen kombinerer historiske kilder – fra 1800-tallets eksperimenter til 1900-tallets patenter – med en kvalitativ dynamisk analyse. Det centrale spørgsmål er friktionens rolle: Hvordan kan toppens massemidtpunkt løftes, samtidig med at rotationen ændrer retning? Seiersen viser, at netop friktion og forskydningen mellem geometrisk centrum og massemidtpunkt muliggør den observerede inversion. Artiklen er både didaktisk inspirerende og teoretisk stimulerende og giver stof til eftertanke om ikke-lineær dynamik i klassiske systemer.
Referencer
[1] J. Perry (1890), "Spinning Tops", Society for promoting Christian knowledge.
[2] J.A. Jacobs (1952), "Note on the Behavior of a Certain Symmetrical Top", Am. J. Phys. 20, 517.
https://doi.org/10.1119/1.1933305
[3] J.L. Synge (1952), "On a case of instability produced by rotation", Phil. Mag. 43, 724.
https://doi.org/10.1080/14786440708520989
[4] C.M. Braams (1952), "The Symmetrical Spherical Top", Nature 170, 31.
https://doi.org/10.1038/170031a0
[5] G.N. Copley (1952), "The Symmetrical Spherical Top", Nature 170, 169.
https://doi.org/10.1038/170169a0
[6] C.M. Braams (1952), "On the Influence of Friction on the Motion of a Top", Physica 18, 503.
https://doi.org/10.1016/S0031-8914(52)80051-5
[7] N.M. Hugenholtz (1952), "On Tops Rising by Friction", Physica 18, 515.
https://doi.org/10.1016/S0031-8914(52)80052-7
[8] C.M. Braams (1954), "The Tippe Top", Am. J. Phys. 22, 568.
https://doi.org/10.1119/1.1933836
[9] W.A. Pliskin (1954), "The Tippe Top (Topsy-Turvy Top)", Am. J. Phys. 22, 28.
https://doi.org/10.1119/1.1933602
[10] A.R. Del Campo (1955), "Tippe Top (Topsy-Turnee Top) Continued", Am. J. Phys. 23, 544.
https://doi.org/10.1119/1.1934091
[11] I.M. Freeman (1956), "The Tippe Top Again", Am. J. Phys. 24, 178.
https://doi.org/10.1119/1.1934180
[12] D.G. Parkyn (1958), "The Rising of Tops with Rounded Pegs", Physica 24, 313.
https://doi.org/10.1016/S0031-8914(58)95049-3
[13] J.B. Hart (1959), "Angular Momentum and Tippe Top", Am. J. Phys. 27, 189.
https://doi.org/10.1119/1.1934800
[14] F.F. Johnson (1960), "The Tippy Top", Am. J. Phys. 28, 406.
https://doi.org/10.1119/1.1935819
[15] V. Güntelberg (1965), "Snurren", Nordisk Matematisk Tidsskrift 13, 15.
[16] J.C. Lauffenburger (1972), "A Large-Scale Demonstration of the Tippe-Top", Am. J. Phys. 40, 1338.
https://doi.org/10.1119/1.1986828
[17] R.J. Cohen (1977), "The Tippe Top Revisited", Am. J. Phys. 45, 12.
https://doi.org/10.1119/1.10926
[18] K.W. Ford (1978), "Why does a finger ring flip", The Physics Teacher 16, 322.
https://doi.org/10.1119/1.2339960
[19] J. Walker (1979), "The Mysterious 'Rattleback': A Stone That Spins in One Direction and Then Reverses", Scientific American 241, 144.
https://doi.org/10.1038/scientificamerican1279-178
[20] J. Walker (1981), "The Physics of Spinning Tops, Including Some Far-Out Ones", Scientific American 244, 134.
[21] H. Leutwyler (1994), "Why some tops tip", Eur. J. Phys. 15, 59.
https://doi.org/10.1088/0143-0807/15/2/003
[22] A.C. Or (1994), "The dynamics of a tippe top", SIAM J. Appl. Math. 54, 597.
https://doi.org/10.1137/S0036139992235123
[23] S. Ebenfeld and F. Scheck (1995), "A new analysis of the tippe top: Asymptotic States and Liapunov stability", Annals of Physics 243, 195.
https://doi.org/10.1006/aphy.1995.1097
[24] N.M. Bou-Rabee, J.E. Marsden, L.A. Romero (2004), "Tippe top inversion as a dissipation-induced instability", SIAM J. Appl. Dyn. Sys. 3, 352.
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