# Noether theorem and first integrals of constrained Lagrangean systems

Mathematica Bohemica (1997)

- Volume: 122, Issue: 3, page 257-265
- ISSN: 0862-7959

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topKrupková, Olga. "Noether theorem and first integrals of constrained Lagrangean systems." Mathematica Bohemica 122.3 (1997): 257-265. <http://eudml.org/doc/248128>.

@article{Krupková1997,

abstract = {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.},

author = {Krupková, Olga},

journal = {Mathematica Bohemica},

keywords = {Lagrangian system; Lepagean two-form; Euler-Lagrange form; singular Lagrangian; constrained system; Noether theorem; symmetry; constants of motion; first integrals; Lagrangian system; Lepagean two-form; Euler-Lagrange form; singular Lagrangian; constrained system; Noether theorem; symmetry; constants of motion; first integrals},

language = {eng},

number = {3},

pages = {257-265},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Noether theorem and first integrals of constrained Lagrangean systems},

url = {http://eudml.org/doc/248128},

volume = {122},

year = {1997},

}

TY - JOUR

AU - Krupková, Olga

TI - Noether theorem and first integrals of constrained Lagrangean systems

JO - Mathematica Bohemica

PY - 1997

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 122

IS - 3

SP - 257

EP - 265

AB - 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.

LA - eng

KW - Lagrangian system; Lepagean two-form; Euler-Lagrange form; singular Lagrangian; constrained system; Noether theorem; symmetry; constants of motion; first integrals; Lagrangian system; Lepagean two-form; Euler-Lagrange form; singular Lagrangian; constrained system; Noether theorem; symmetry; constants of motion; first integrals

UR - http://eudml.org/doc/248128

ER -

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