### Abstract

Some solutions of three body problem with equal masses are first considered in form space. The solutions in usual euclidean space may be restored from these form space solutions. If constant energy h < 0, the trajectories are located inside of Hill's surface. Without loss of generality due to scale symmetry we can set h = -1. Such surface has a simple form in form space. Solutions of isosceles and rectilinear three body problems lie within Hill's curve; periodic solutions of free fall three body problem start in one point of this curve, and finish in another. The solutions are illustrated by number of figures.

Original language | English |
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Title of host publication | 8th Polyakhov's Reading |

Subtitle of host publication | Proceedings of the International Scientific Conference on Mechanics |

Editors | Elena V. Kustova, Gennady A. Leonov, Mikhail P. Yushkov, Nikita F. Morosov, Mariia A. Mekhonoshina |

Publisher | American Institute of Physics |

Volume | 1959 |

ISBN (Electronic) | 9780735416604 |

DOIs | |

Publication status | Published - 2 May 2018 |

Event | International Scientific Conference on Mechanics: 8th Polyakhov's Reading - Saint Petersburg Duration: 29 Jan 2018 → 2 Feb 2018 |

### Conference

Conference | International Scientific Conference on Mechanics: 8th Polyakhov's Reading |
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Country | Russian Federation |

City | Saint Petersburg |

Period | 29/01/18 → 2/02/18 |

### Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics*(Vol. 1959). [040024] American Institute of Physics. https://doi.org/10.1063/1.5034627

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*8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics.*vol. 1959, 040024, American Institute of Physics, Saint Petersburg, 29/01/18. https://doi.org/10.1063/1.5034627

**Some solutions of the general three body problem in form space.** / Titov, Vladimir.

Research output › › peer-review

TY - GEN

T1 - Some solutions of the general three body problem in form space

AU - Titov, Vladimir

PY - 2018/5/2

Y1 - 2018/5/2

N2 - Some solutions of three body problem with equal masses are first considered in form space. The solutions in usual euclidean space may be restored from these form space solutions. If constant energy h < 0, the trajectories are located inside of Hill's surface. Without loss of generality due to scale symmetry we can set h = -1. Such surface has a simple form in form space. Solutions of isosceles and rectilinear three body problems lie within Hill's curve; periodic solutions of free fall three body problem start in one point of this curve, and finish in another. The solutions are illustrated by number of figures.

AB - Some solutions of three body problem with equal masses are first considered in form space. The solutions in usual euclidean space may be restored from these form space solutions. If constant energy h < 0, the trajectories are located inside of Hill's surface. Without loss of generality due to scale symmetry we can set h = -1. Such surface has a simple form in form space. Solutions of isosceles and rectilinear three body problems lie within Hill's curve; periodic solutions of free fall three body problem start in one point of this curve, and finish in another. The solutions are illustrated by number of figures.

UR - http://www.scopus.com/inward/record.url?scp=85047210676&partnerID=8YFLogxK

U2 - 10.1063/1.5034627

DO - 10.1063/1.5034627

M3 - Conference contribution

VL - 1959

BT - 8th Polyakhov's Reading

A2 - Kustova, Elena V.

A2 - Leonov, Gennady A.

A2 - Yushkov, Mikhail P.

A2 - Morosov, Nikita F.

A2 - Mekhonoshina, Mariia A.

PB - American Institute of Physics

ER -