Non-integrability of the equations of heavy gyrostat

Ljubomir Gavrilov

Compositio Mathematica (1992)

  • Volume: 82, Issue: 3, page 275-291
  • ISSN: 0010-437X

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Gavrilov, Ljubomir. "Non-integrability of the equations of heavy gyrostat." Compositio Mathematica 82.3 (1992): 275-291. <http://eudml.org/doc/90154>.

@article{Gavrilov1992,
author = {Gavrilov, Ljubomir},
journal = {Compositio Mathematica},
keywords = {Zhukovsky case; Lagrange case; Yehia case; additional algebraic first integral},
language = {eng},
number = {3},
pages = {275-291},
publisher = {Kluwer Academic Publishers},
title = {Non-integrability of the equations of heavy gyrostat},
url = {http://eudml.org/doc/90154},
volume = {82},
year = {1992},
}

TY - JOUR
AU - Gavrilov, Ljubomir
TI - Non-integrability of the equations of heavy gyrostat
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 82
IS - 3
SP - 275
EP - 291
LA - eng
KW - Zhukovsky case; Lagrange case; Yehia case; additional algebraic first integral
UR - http://eudml.org/doc/90154
ER -

References

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  1. [1] Ablowitz, M.J., Ramani, A. and Segur, H.: J. Math.Phys.21 (1980), 715. Zbl0445.35056MR565716
  2. [2] Alder, M. and van Moerbeke, P.: Algebraic Completely Integrable Systems: A Systematic Approach, Academic Press, to appear. 
  3. [3] Bruns, H.: Acta Math.11 (1887), 25-96. JFM19.0935.01
  4. [4] Gavrilov, L.: Non-integrability of a class of differential equations which are not of Painlevé type, Compt. Rend. Acad. Bulg. Sci.41 (1988), 21-24. Zbl0649.34013MR944555
  5. [5] Gavrilov, L.: On the integrable cases of the equations of heavy gyrostat, Annuaire de l'Universite de Sofia Mécanique80 (1986) in Russian. 
  6. [6] Gavrilov, L.: Remarks on the equations of heavy gyrostat, Compt. Rend. Acad. Bulg. Sci.42 (1989), 17-20. Zbl0668.70007MR1020855
  7. [7] Golubev, V.V.: Lectures on the integration of equations of motion of a rigid body about a fixed point,Haifa: Israel, 1960. Zbl0122.18701MR116511
  8. [8] Gorr, G.V.: Kudryashova, L.V. and Stepanova, L.A.: Classical problems in rigid body dynamics,Naukova Dumka: Kiev, 1978 in Russian. 
  9. [9] Griffiths, P. and Harris, J.: Principles of Algebraic Geometry, Wiley-Interscience, New York (1978). Zbl0408.14001MR507725
  10. [10] Horn, J.: J. Reine und Angew. Math116 (1896), 265-306 and J. Reine und Angew. Math.117 (1897), 104-128, 254-266. JFM27.0260.01
  11. [11] Husson, Ed.: Recherche des intégrales algébriques dans le mouvement d'un solide pesant autour d'un point fixe, Ann. Fac. Sci. Univ. Toulouse Serie28 (1906), 73-152 and Acta Math.31 (1907), 71. Zbl37.0746.01JFM37.0746.01
  12. [12] Keis, I.A.: PMM USSR28 (1964), 633-639. Zbl0136.21902
  13. [13] Kozlov, V.V.: Methods for Qualitative Analysis in Rigid Body Dynamics, Moscow University Press, Moscow (1980). Zbl0557.70009MR598628
  14. [14] Lesfari, A.: Abelian surfaces and Kowalewski's top, Ann. Scient. Ec. Norm. Sup.4e série 21 (1988), 193-223. Zbl0667.58019MR956766
  15. [15] Yehia, H.M.: J. Mecan. Theor. Appl.5 (1986), 747-754. Zbl0619.70005MR852183
  16. [16] Yehia, H.M.: Mech. Res. Commun.13 (1986), 169-172. Zbl0606.70008MR852199
  17. [17] Yoshida, H.: Celest. Mech.31 (1983), 363-379 and 31 (1983), 381-399. Zbl0556.70014MR737804
  18. [18] Ziglin, S.L.: Funct. Anal. Appl.16 (1983), 181-189 and 17 (1983), 6-17. Zbl0518.58016

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