The twisting tennis racket

Abstract

This paper describes, analyzes, and explains a novel twisting phenomenon which occurs in a triaxial rigid body (such as a tennis racket) when it is rotating about an axis initially near its unstable intermediate principal axis.

This is a preview of subscription content, log in to check access.

References

  1. Abramowitz, M., and Stegun, I. A. (eds.) (1964).Handbook of Mathematical Functions, Applied Mathematics Series, Vol. 55, National Bureau of Standards, Washington, D.C.

    Google Scholar 

  2. Arnol'd, V. I. (1978).Mathematical Methods of Classical Mechanics, Springer-Verlag, New York.

    Google Scholar 

  3. Brody, H. (1985). The moment of inertia of a tennis racket.Phys. Teach. April, 213–216.

    Google Scholar 

  4. Colley, S. J. (1987). The tumbling box.Am. Math. Month. 94, 62–68. [See also (1987). Letter to the editor. Am. Math. Month.94, 646].

    Google Scholar 

  5. Goldstein, H. (1950).Classical Mechanics, Addison-Wesley, Reading, Mass.

    Google Scholar 

  6. Gradshteyn, I. S., and Ryzhik, I. M. (1980).Table of Integrals, Series and Products, corrected and enlarged ed., Academic Press, New York.

    Google Scholar 

  7. Klein, F., and Sommerfeld, A. (1897–1910).Über die Theorie des Kreisels (4 vols.), B. G. Teubner, Leipzig.

    Google Scholar 

  8. Landau, L. D., and Lifshitz, E. M. (1976).Mechanics, 3rd ed., Pergamon Press, Oxford.

    Google Scholar 

  9. Rauch, H., and Lebowitz, A. (1973).Elliptic Functions, Theta Functions, and Riemann Surfaces, Williams and Wilkins, Baltimore.

    Google Scholar 

  10. Tricomi, F. G. (1953).Differential Equations, Blackie and Son, London.

    Google Scholar 

  11. Webster, A. G. (1920).The Dynamics of Particles and of Rigid, Elastic, and Fluid Bodies, Stechert-Hafner, New York.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Carmen C. Chicone.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ashbaugh, M.S., Chicone, C.C. & Cushman, R.H. The twisting tennis racket. J Dyn Diff Equat 3, 67–85 (1991). https://doi.org/10.1007/BF01049489

Download citation

Key words

  • Euler equations
  • rigid body motion
  • Euler angles
  • Eulerian wobble

1980 AMS(MOS) mathematics subject classifications

  • 70E15
  • 58F05