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Unimodularity and preservation of volumes in nonholonomic mechanics

Autor
Fedorov, Y.; García, L.; Marrero, J.
Tipus d'activitat
Article en revista
Revista
Journal of nonlinear science
Data de publicació
2015-02-01
Volum
25
Número
1
Pàgina inicial
203
Pàgina final
246
DOI
https://doi.org/10.1007/s00332-014-9227-4 Obrir en finestra nova
Projecte finançador
DINAMICA ASOCIADA A CONEXIONES ENTRE OBJETOS INVARIANTES. APLICACIONES A
Red: Geometría, Mecánica y Control
URL
http://link.springer.com/article/10.1007%2Fs00332-014-9227-4 Obrir en finestra nova
Resum
The equations of motion of a mechanical system subjected to nonholonomic linear constraints can be formulated in terms of a linear almost Poisson structure in a vector bundle. We study the existence of invariant measures for the system in terms of the unimodularity of this structure. In the presence of symmetries, our approach allows us to give necessary and sufficient conditions for the existence of an invariant volume, which unify and improve results existing in the literature. We present an a...
Paraules clau
Invariant volume forms, Linear almost Poisson structure, Modular vector field, Nonholonomic mechanical systems, Reduction, Symmetries, Unimodularity, dynamics, euler-poincare equations, generalized chaplygin systems, horizontal plane, invariant-measures, lie algebroids, quadratic poisson structures, rigid-body, suslov problem, symmetry
Grup de recerca
SD - Sistemes Dinàmics de la UPC

Participants

  • Fedorov Kuzmin, Yury  (autor)
  • García Naranjo, Luis C.  (autor)
  • Marrero Gonzalez, Juan Carlos  (autor)