Geodesic
Non-holonomic dynamics and Poisson geometry
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 3, pp. 481-538

Voir la notice de l'article provenant de la source Math-Net.Ru

This is a survey of basic facts presently known about non-linear Poisson structures in the analysis of integrable systems in non-holonomic mechanics. It is shown that by using the theory of Poisson deformations it is possible to reduce various non-holonomic systems to dynamical systems on well-understood phase spaces equipped with linear Lie–Poisson brackets. As a result, not only can different non-holonomic systems be compared, but also fairly advanced methods of Poisson geometry and topology can be used for investigating them. Bibliography: 95 titles.
Keywords: non-holonomic systems, Chaplygin ball, Suslov system, Veselova system.
Mots-clés : Poisson bracket 
@article{RM_2014_69_3_a3,
     author = {A. V. Borisov and I. S. Mamaev and A. V. Tsiganov},
     title = {Non-holonomic dynamics and {Poisson} geometry},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {481--538},
     publisher = {mathdoc},
     volume = {69},
     number = {3},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2014_69_3_a3/}
}
TY  - JOUR
AU  - A. V. Borisov
AU  - I. S. Mamaev
AU  - A. V. Tsiganov
TI  - Non-holonomic dynamics and Poisson geometry
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2014
SP  - 481
EP  - 538
VL  - 69
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RM_2014_69_3_a3/
LA  - en
ID  - RM_2014_69_3_a3
ER  - 
%0 Journal Article
%A A. V. Borisov
%A I. S. Mamaev
%A A. V. Tsiganov
%T Non-holonomic dynamics and Poisson geometry
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2014
%P 481-538
%V 69
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RM_2014_69_3_a3/
%G en
%F RM_2014_69_3_a3
A. V. Borisov; I. S. Mamaev; A. V. Tsiganov. Non-holonomic dynamics and Poisson geometry. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 3, pp. 481-538. http://geodesic.mathdoc.fr/item/RM_2014_69_3_a3/