### Abstract

There are various ways for introducing the concept of the instantaneous angular velocity vector. In this paper we propose a method based on introducing of this concept by construction of the solution for the system of kinematic equations. These equations connect the function vectors defining the motion of the basis, and their derivatives. Necessary and sufficient conditions for the existence and uniqueness of the solution of this system are established. The instantaneous angular velocity vector is a solution of the algebraic system of equations. It is built explicitly. The derived formulas for the angular velocity vector generalize the earlier results, both for a basis of an affine oblique coordinate system and for an orthonormal basis.

Original language | English |
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Title of host publication | EIGHTH POLYAKHOV'S READING |

Subtitle of host publication | Proceedings of the International Scientific Conference on Mechanics, 8th Polyakhov's Reading |

Editors | E Kustova, G Leonov, N Morosov, M Yushkov, M Mekhonoshina |

Publisher | American Institute of Physics |

Number of pages | 7 |

Volume | 1959 |

ISBN (Electronic) | 9780735416604 |

DOIs | |

Publication status | Published - 2 May 2018 |

Event | Восьмые Поляховские чтения: международная научная конференция по механике - Старый Петергоф, Saint Petersburg Duration: 29 Jan 2018 → 2 Feb 2018 Conference number: 8 https://events.spbu.ru/events/polyakhov_readings http://nanomat.spbu.ru/en/node/175 http://nanomat.spbu.ru/ru/node/192 http://spbu.ru/news-events/calendar/viii-polyahovskie-chteniya |

### Publication series

Name | AIP Conference Proceedings |
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Publisher | AMER INST PHYSICS |

Volume | 1959 |

ISSN (Print) | 0094-243X |

### Conference

Conference | International Scientific Conference on Mechanics - Eighth Polyakhov's Reading |
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Country | Russian Federation |

City | Saint Petersburg |

Period | 29/01/18 → 2/02/18 |

Internet address |

### Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics, 8th Polyakhov's Reading*(Vol. 1959). [030008] (AIP Conference Proceedings; Vol. 1959). American Institute of Physics. https://doi.org/10.1063/1.5034588