Generalized Birkhoffian realization of nonholonomic systems
Yong-Xin Guo; Chang Liu; Shi-Xing Liu
Communications in Mathematics (2010)
- Volume: 18, Issue: 1, page 21-35
- ISSN: 1804-1388
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topGuo, Yong-Xin, Liu, Chang, and Liu, Shi-Xing. "Generalized Birkhoffian realization of nonholonomic systems." Communications in Mathematics 18.1 (2010): 21-35. <http://eudml.org/doc/196944>.
@article{Guo2010,
abstract = {Based on the Cauchy-Kowalevski theorem for a system of partial differential equations to be integrable, a kind of generalized Birkhoffian systems (GBSs) with local, analytic properties are put forward, whose manifold admits a presymplectic structure described by a closed 2-form which is equivalent to the self-adjointness of the GBSs. Their relations with Birkhoffian systems, generalized Hamiltonian systems are investigated in detail. Analytic, algebraic and geometric properties of GBSs are formulated, together with their integration methods induced from the Birkhoffian systems. As an important example, nonholonomic systems are reduced into GBSs, which gives a new approach to some open problems of nonholonomic mechanics.},
author = {Guo, Yong-Xin, Liu, Chang, Liu, Shi-Xing},
journal = {Communications in Mathematics},
keywords = {inverse problem; self-adjointness condition},
language = {eng},
number = {1},
pages = {21-35},
publisher = {University of Ostrava},
title = {Generalized Birkhoffian realization of nonholonomic systems},
url = {http://eudml.org/doc/196944},
volume = {18},
year = {2010},
}
TY - JOUR
AU - Guo, Yong-Xin
AU - Liu, Chang
AU - Liu, Shi-Xing
TI - Generalized Birkhoffian realization of nonholonomic systems
JO - Communications in Mathematics
PY - 2010
PB - University of Ostrava
VL - 18
IS - 1
SP - 21
EP - 35
AB - Based on the Cauchy-Kowalevski theorem for a system of partial differential equations to be integrable, a kind of generalized Birkhoffian systems (GBSs) with local, analytic properties are put forward, whose manifold admits a presymplectic structure described by a closed 2-form which is equivalent to the self-adjointness of the GBSs. Their relations with Birkhoffian systems, generalized Hamiltonian systems are investigated in detail. Analytic, algebraic and geometric properties of GBSs are formulated, together with their integration methods induced from the Birkhoffian systems. As an important example, nonholonomic systems are reduced into GBSs, which gives a new approach to some open problems of nonholonomic mechanics.
LA - eng
KW - inverse problem; self-adjointness condition
UR - http://eudml.org/doc/196944
ER -
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