Celestial Mechanics and Dynamical Astronomy

, Volume 59, Issue 2, pp 149–159 | Cite as

Elements of spin motion

  • Toshio Fukushima
  • Hideharu Ishizaki
Article

Abstract

For use in numerical studies of rotational motion, a set of elements is introduced for the torque-free rotational motion of a rigid body around its barycenter. The elements are defined as the initial values of a modification of the Andoyer canonical variables. A computational procedure is obtained for determining these elements from the combination of the spin angular momentum vector and a triad defining the orientation of the rigid body. A numerical experiment shows that the errors of transformation between the elements and variables are sufficiently small. The errors increase linearly with time for some elements and quadratically for some others.

Key words

Andoyer canonical variables elliptic functions and integrals torque-free rotational motion numerical computation spin elements 

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References

  1. Andoyer, H.: 1923,Cours de Mechanique Celeste, Vol. 1, Gauthier-Villars, Paris, p. 54.Google Scholar
  2. Burlisch, R.: 1969,Numerical Mathematik 13, 266.Google Scholar
  3. Byrd, P. F. and Friedman, M. D.: 1954,Handbook of Elliptic Integrals of Engineers and Physicists, Springer-Verlag, Berlin.Google Scholar
  4. Deprit, A.: 1967,Amer. J. Phys. 35, 424.Google Scholar
  5. Fukushima, T. and Ishizaki, H.: 1993, ‘Numerical Computations of Incomplete Elliptic Integrals of a General Form’,Celestial Mechanics and Dynamical Astronomy (accepted).Google Scholar
  6. Jupp, A. H.: 1974,Celestial Mechanics 9, 3.Google Scholar
  7. Kinoshita, H.: 1972,Publ. Astron. Soc. Japan 24, 423.Google Scholar
  8. Kinoshita, H.: 1992,Celestial Mechanics and Dynamical Astronomy 53, 365.Google Scholar
  9. Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T.: 1986,Numerical Recipes, Cambridge Univ. Press, Cambridge, Section 6.7.Google Scholar
  10. Whittaker, E. T.: 1937,A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, 4th ed., Cambridge Univ. Press, Cambridge, Section 69.Google Scholar
  11. Wolfram, S.: 1991,Mathematica: A System for Doing Mathematics by Computer, 2nd ed., Addison-Wesley Publ. Co. Inc., Redwood City, Section 3.2.11.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Toshio Fukushima
    • 1
  • Hideharu Ishizaki
    • 1
  1. 1.National Astronomical ObservatoryMitaka, TokyoJapan

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