Geodesic
The Rigid Body Dynamics: Classical and Algebro-geometric Integration
Zbornik radova, Tome 16 (2013) no. 24, p. 5 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The basic notion for a motion of a heavy rigid body fixed at a point in three-dimensional space as well as its higher-dimensional generalizations are presented. On a basis of the Lax representation, the algebro-geometric integration procedure for one of the classical cases of motion of three-dimensional rigid body - the Hess-Appel'rot system is given. The classical integration in Hess coordinates is presented also. For higher-dimensional generalizations, the special attention is paid in dimension four. The L-A pairs and the classical integration procedures for completely integrable four-dimensional rigid body so called the Lagrange bitop as well as for four-dimensional generalization of Hess-Appel'rot system are given. An $n$-dimensional generalization of the Hess-Appel'rot system is also presented and its Lax representation is given. Starting from another Lax representation for the Hess-Appel'rot system, a family of dynamical systems on $e(3)$ is constructed. For five cases from the family, the classical and algebro-geometric integration procedures are presented. The four-dimensional generalizations for the Kirchhoff and the Chaplygin cases of motion of rigid body in ideal fluid are defined. The results presented in the paper are part of results obtained in the last decade.
Classification : 70E17 70E40 70E45 70H06 37J35
Keywords: rigid body motion, Lax representation, algebro-geometric integration procedure, Baker-Akhiezer function 
@article{ZR_2013_16_24_a0,
     author = {Borislav Gaji\'c},
     title = {The {Rigid} {Body} {Dynamics:} {Classical} and {Algebro-geometric} {Integration}},
     journal = {Zbornik radova},
     pages = {5 },
     publisher = {mathdoc},
     volume = {16},
     number = {24},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZR_2013_16_24_a0/}
}
TY  - JOUR
AU  - Borislav Gajić
TI  - The Rigid Body Dynamics: Classical and Algebro-geometric Integration
JO  - Zbornik radova
PY  - 2013
SP  - 5 
VL  - 16
IS  - 24
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZR_2013_16_24_a0/
LA  - en
ID  - ZR_2013_16_24_a0
ER  - 
%0 Journal Article
%A Borislav Gajić
%T The Rigid Body Dynamics: Classical and Algebro-geometric Integration
%J Zbornik radova
%D 2013
%P 5 
%V 16
%N 24
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZR_2013_16_24_a0/
%G en
%F ZR_2013_16_24_a0
Borislav Gajić. The Rigid Body Dynamics: Classical and Algebro-geometric Integration. Zbornik radova, Tome 16 (2013) no. 24, p. 5 . http://geodesic.mathdoc.fr/item/ZR_2013_16_24_a0/