On the analytic non-integrability of the Rattleback problem
H. R. Dullin[1]; A.V. Tsygvintsev[2]
- [1] School of Mathematics and Statitics F07. University of Sydney NSW 2006. Sydney. Australia.
- [2] Unité de mathématiques pures et appliquées. École Normale Supérieure de Lyon 46, allée d’Italie, Lyon F–69364 Lyon Cedex 07, France.
Annales de la faculté des sciences de Toulouse Mathématiques (2008)
- Volume: 17, Issue: 3, page 495-517
- ISSN: 0240-2963
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topDullin, H. R., and Tsygvintsev, A.V.. "On the analytic non-integrability of the Rattleback problem." Annales de la faculté des sciences de Toulouse Mathématiques 17.3 (2008): 495-517. <http://eudml.org/doc/10094>.
@article{Dullin2008,
abstract = {We establish the analytic non-integrability of the nonholonomic ellipsoidal rattleback model for a large class of parameter values. Our approach is based on the study of the monodromy group of the normal variational equations around a particular orbit. The imbedding of the equations of the heavy rigid body into the rattleback model is discussed.},
affiliation = {School of Mathematics and Statitics F07. University of Sydney NSW 2006. Sydney. Australia.; Unité de mathématiques pures et appliquées. École Normale Supérieure de Lyon 46, allée d’Italie, Lyon F–69364 Lyon Cedex 07, France.},
author = {Dullin, H. R., Tsygvintsev, A.V.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {nonholonomic ellipsoidal model; variational equations; monodromy group},
language = {eng},
month = {6},
number = {3},
pages = {495-517},
publisher = {Université Paul Sabatier, Toulouse},
title = {On the analytic non-integrability of the Rattleback problem},
url = {http://eudml.org/doc/10094},
volume = {17},
year = {2008},
}
TY - JOUR
AU - Dullin, H. R.
AU - Tsygvintsev, A.V.
TI - On the analytic non-integrability of the Rattleback problem
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2008/6//
PB - Université Paul Sabatier, Toulouse
VL - 17
IS - 3
SP - 495
EP - 517
AB - We establish the analytic non-integrability of the nonholonomic ellipsoidal rattleback model for a large class of parameter values. Our approach is based on the study of the monodromy group of the normal variational equations around a particular orbit. The imbedding of the equations of the heavy rigid body into the rattleback model is discussed.
LA - eng
KW - nonholonomic ellipsoidal model; variational equations; monodromy group
UR - http://eudml.org/doc/10094
ER -
References
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- Tsygvintsev (A.).— Non-existence of new meromorphic first integrals in the planar three-body problem. Celestial Mech. Dynam. Astronom. 86, no. 3, 237–247 (2003). Zbl1062.70024MR1988844
- Morales-Ruiz (J.).— Differential Galois theory and non–integrability of Hamiltonian systems, Birkhäuser Verlag, Basel (1999). Zbl0934.12003MR1713573
- Ziglin (S.L.).— Branching of solutions and non-existence of first integrals in Hamiltonian Mechanics I, Funct. Anal. Appl. 16, 181–189 (1982). Zbl0524.58015
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