### Abstract

In order to characterize the systems of second-order ODEs which admit a regular Lagrangian function, Noether symmetries for the geodesic equations of the canonical linear connection on Lie groups of dimension three or less are obtained, so the characterization of these geodesic equations through their Noether's symmetries Lie Algebras is investigated. The corresponding conservation laws and the first integral for each geodesics are constructed.

Original language | English |
---|---|

Pages (from-to) | 311-318 |

Number of pages | 8 |

Journal | Applied Mathematics and Information Sciences |

Volume | 7 |

Issue number | 1 |

Publication status | Published - Jan 2013 |

Externally published | Yes |

### Fingerprint

### Keywords

- Canonical linear connection on lie groups
- Conservations laws
- Geodesic equations
- Inverse problem of lagrangian dynamics
- Systems of second-order ODEs

### ASJC Scopus subject areas

- Applied Mathematics
- Numerical Analysis
- Analysis
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

*Applied Mathematics and Information Sciences*,

*7*(1), 311-318.

**Conservation laws for the geodesic equations of the canonical connection on Lie groups in dimensions two and three.** / Ghanam, Ryad; Al-Dweik, Ahmad Y.

Research output: Contribution to journal › Article

*Applied Mathematics and Information Sciences*, vol. 7, no. 1, pp. 311-318.

}

TY - JOUR

T1 - Conservation laws for the geodesic equations of the canonical connection on Lie groups in dimensions two and three

AU - Ghanam, Ryad

AU - Al-Dweik, Ahmad Y.

PY - 2013/1

Y1 - 2013/1

N2 - In order to characterize the systems of second-order ODEs which admit a regular Lagrangian function, Noether symmetries for the geodesic equations of the canonical linear connection on Lie groups of dimension three or less are obtained, so the characterization of these geodesic equations through their Noether's symmetries Lie Algebras is investigated. The corresponding conservation laws and the first integral for each geodesics are constructed.

AB - In order to characterize the systems of second-order ODEs which admit a regular Lagrangian function, Noether symmetries for the geodesic equations of the canonical linear connection on Lie groups of dimension three or less are obtained, so the characterization of these geodesic equations through their Noether's symmetries Lie Algebras is investigated. The corresponding conservation laws and the first integral for each geodesics are constructed.

KW - Canonical linear connection on lie groups

KW - Conservations laws

KW - Geodesic equations

KW - Inverse problem of lagrangian dynamics

KW - Systems of second-order ODEs

UR - http://www.scopus.com/inward/record.url?scp=84873448362&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873448362&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84873448362

VL - 7

SP - 311

EP - 318

JO - Applied Mathematics and Information Sciences

JF - Applied Mathematics and Information Sciences

SN - 1935-0090

IS - 1

ER -