### 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) |
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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 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Bouarroudj, S., & Konstein, S. E. (2020). SO(4)-symmetry of mechanical systems with 3 degrees of freedom.

*Journal of Nonlinear Mathematical Physics*,*27*(1), 162-169. https://doi.org/10.1080/14029251.2020.1683997