### Abstract

We answered an old question: does there exist a mechanical system with 3 degrees of freedom, except for the Coulomb system, which has 6 first integrals generating the Lie algebra (Figure presented.) (4) by means of the Poisson brackets? A system which is not centrally symmetric, but has 6 first integrals generating Lie algebra (Figure presented.) (4), is presented. It is shown also that not every mechanical system with 3 degrees of freedom has first integrals generating (Figure presented.) (4).

Original language | English (US) |
---|---|

Pages (from-to) | 162-169 |

Number of pages | 8 |

Journal | Journal of Nonlinear Mathematical Physics |

Volume | 27 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2 2020 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Nonlinear Mathematical Physics*,

*27*(1), 162-169. https://doi.org/10.1080/14029251.2020.1683997

**SO(4)-symmetry of mechanical systems with 3 degrees of freedom.** / Bouarroudj, Sofiane; Konstein, Semyon E.

Research output: Contribution to journal › Article

*Journal of Nonlinear Mathematical Physics*, vol. 27, no. 1, pp. 162-169. https://doi.org/10.1080/14029251.2020.1683997

}

TY - JOUR

T1 - SO(4)-symmetry of mechanical systems with 3 degrees of freedom

AU - Bouarroudj, Sofiane

AU - Konstein, Semyon E.

PY - 2020/1/2

Y1 - 2020/1/2

N2 - We answered an old question: does there exist a mechanical system with 3 degrees of freedom, except for the Coulomb system, which has 6 first integrals generating the Lie algebra (Figure presented.) (4) by means of the Poisson brackets? A system which is not centrally symmetric, but has 6 first integrals generating Lie algebra (Figure presented.) (4), is presented. It is shown also that not every mechanical system with 3 degrees of freedom has first integrals generating (Figure presented.) (4).

AB - We answered an old question: does there exist a mechanical system with 3 degrees of freedom, except for the Coulomb system, which has 6 first integrals generating the Lie algebra (Figure presented.) (4) by means of the Poisson brackets? A system which is not centrally symmetric, but has 6 first integrals generating Lie algebra (Figure presented.) (4), is presented. It is shown also that not every mechanical system with 3 degrees of freedom has first integrals generating (Figure presented.) (4).

UR - http://www.scopus.com/inward/record.url?scp=85074142795&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074142795&partnerID=8YFLogxK

U2 - 10.1080/14029251.2020.1683997

DO - 10.1080/14029251.2020.1683997

M3 - Article

AN - SCOPUS:85074142795

VL - 27

SP - 162

EP - 169

JO - Journal of Nonlinear Mathematical Physics

JF - Journal of Nonlinear Mathematical Physics

SN - 1402-9251

IS - 1

ER -