Tumbling cards

Physics of Fluids

Volumn 11, Issue 1, 1999, Pages 1-3

  Mahadevan, L ^a   Ryu, William S ^b,c   Samuel, Aravindhan D T ^b,c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b HARVARD UNIVERSITY   (United States)

^c HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346466060     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869919     Document Type: Article

References (19)

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2. J. C. Maxwell, Scientific Papers and Letters of J. C. Maxwell (Cambridge University Press, Cambridge, 1990), p. 560. In one of the letters, Maxwell begins by saying "As to teh strip of paper, I suppose many must have dropped since the invention of paper, but fruitlessly, quia carent vate sacro," quoting Horace. In another letter by Kelvin to Stokes, we find the statement "I thought first, and am now again nearly convinced, that the generation of rotary motion here is indexplicable without taking into account the viscosity of air."
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12. L. Mahadevan, H. Aref, and S. W. Jones, "Comment on 'Behavior of a Falling Paper' (with reply)," Phys. Rev. Lett. 75, 1420 (1995).
13. L. Mahadevan, "Tumbling of a falling card," C.R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. 323, 729 (1996).
14. S. B. Field, M. Klaus, M. G. Moore, and F. Nori, "Chaotic dynamics of falling disks," Nature (London) 388, 252 (1997).
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16. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer, Berlin, 1983).
17. This picture is reminiscent of the behavior of a conservative pendulum which is capable of oscillations or rotations depending on its initial energy; the main difference is that the angular variable describing the orientation of the strip is twice that of the analogous pendulum Ref. 19.
18. Modern Developments in Fluid Dynamics, edited by S. Goldstein (Oxford University Press, New York, 1938), Vol. II, Chap. 10.
19. H. Lamb, Hydrodynamics (Dover, New York, 1945), Chap. X.