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Title: Noether theorem and first integrals of constrained Lagrangean systems (English)
Author: Krupková, Olga
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 122
Issue: 3
Year: 1997
Pages: 257-265
Summary lang: English
Category: math
Summary: The dynamics of singular Lagrangean systems is described by a distribution the rank of which is greater than one and may be non-constant. Consequently, these systems possess two kinds of conserved functions, namely, functions which are constant along extremals (constants of the motion), and functions which are constant on integral manifolds of the corresponding distribution (first integrals). It is known that with the help of the (First) Noether theorem one gets constants of the motion. In this paper it is shown that every constant of the motion obtained from the Noether theorem is a first integral; thus, Noether theorem can be used for an effective integration of the corresponding distribution. (English)
Keyword: Lagrangian system
Keyword: Lepagean two-form
Keyword: Euler-Lagrange form
Keyword: singular Lagrangian
Keyword: constrained system
Keyword: Noether theorem
Keyword: symmetry
Keyword: constants of motion
Keyword: first integrals
MSC: 37B99
MSC: 58F05
MSC: 58F35
MSC: 70H03
MSC: 70H33
MSC: 70H35
idZBL: Zbl 0897.58024
idMR: MR1600644
DOI: 10.21136/MB.1997.126152
Date available: 2009-09-24T21:26:09Z
Last updated: 2020-07-29
Stable URL:
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